Palm trees are monocots and are therefore related to grasses, however they are not grasses themselves. Monocots are a really broad group though. Kinda like saying a certain animal is a mammal. Important distinction but still very broad.

Trees are not a taxonomic group. It’s rather a description of characteristics the most important of which is having a woody trunk. For example there are tree legumes and non-tree legumes. A species of tree can therefore be more closely related to a non-tree than to other trees. However it’s totally true bamboo is not a tree. A grass could in theory however hit all the characteristics that are required to be tree and would then be considered as such, however no such grass happens to exist.

Bamboo is kind of a tree in this case which is an area I know more about and I think many of these factors would apply to bamboo as well. First forests used to actually be more rare than today before humans came along. Europe and North America was covered by endless plains which were grazed by huge numbers of ruminant animals. Any tree that would try to grow would get grazed before it could grow so tall that the animals couldn’t eat it anymore. That’s why grass thrives in such an environment, it’s practically made to get grazed. Once cut it quickly grows back again. Once ancient humans came along and hunted most of the grazing animals extinct forest suddenly started spreading like crazy until almost the entirety of Europe was forested (which was then to a large extent deforested again after agriculture was invented). Grass simply can’t compete against trees for sunlight. Therefore I would expect less or none bamboo in areas with a huge grazing wild life populations. And I don’t mean animals that would eat the leaves, but the ones that would eat the new seedling.

Another thing that limits trees is moisture. In general the drier the climate the less beneficial it is to be a tree. That’s because deep roots are of no benefit in dry climates (but they are of huge benefit in humid climates during drought). Grass which generally have very shallow roots suck up all the rain before it can penetrate deep into the soil while deep tree roots never get any significant amount of water. Trees handle drought well but constant dryness is very detrimental for them. Dry areas also tend to have wild fires which also hamper trees. It’s simply better to be a grass (if moderately dry) or a cactus like plant if it’s extremely dry.

Another factor is soil conditions. Now I don’t know what soil bamboo prefers but I doubt it’s all soil. Soil can have huge impacts on things like pH and water availability. For example in far Northern Europe where I live you can tell that you are standing on sandy soil if all around you are spruces and pines. If you however see lots of leaf trees you are probably on a silt and clay soil. This is because conifers handle both dry and sour soil better than the local leaf trees which leads to more conifers on sand. Bamboo is probably also limited to a certain soil condition.

I hope that can at least help you develop more theories on why bamboo is not everywhere. Something important to remember is that just because a plant can grow well in a certain location doesn’t mean it will be found there. That’s because plants are always in fierce competition. I bet bamboo if intentionally planted and cared for could thrive in lots more places than its found naturally, but it just happens to not be the best plant in that location, meaning it’s outcompeted over long time scales.

Alfalfa is drought tolerant compared to other forage legumes like clover. This means that during drought the alfalfa will fare better and also yield better than clover or a grass like Timothy or blue grass. However as you can see pasture is also on that list you linked. Fodder crops are harvested for their entire biomass above ground and the amount of biomass is very large. It’s a very productive crop and makes a lot of fodder and this fodder is mostly water. Therefore it takes a lot of water to grow. The water required is not extreme in any way however and where I live alfalfa is a rainfed crop that only very rarely has any water deficiency symptoms. The extreme amounts of water applied to alfalfa in the south east of the USA is only because of the desert climate there. Growing beans, corn or potatoes there also requires insane amounts of water. If potatoes were chiefly grown in the desert southeast you bet you would see news articles going around about how terrible potatoes are. In the end it’s only a matter of matching the right crop to the right climate. Even the most water hungry crop on earth will not require irrigation in the most rainy place on earth.

Alfalfa is a great crop. It has deep roots which store carbon in the soil, it is drought tolerant, it’s high yielding and it’s nitrogen fixating meaning it improves the soil quality and does not require nitrogen fertilizer which normally is a huge carbon footprint. Overall fantastic crop if you need fodder for ruminant animals. The big problem is farming it on an absurd scale in the middle of the damn desert. Alfalfa does not require irrigation in regions with ample rainfall.

Largest problem with manure, including human manure in this case, is the algal blooms that result from the phosphorous and nitrogen getting into water. That can cause eutrophication that can cause the collapse of entire ecosystems. But of course with proper sewage treatment this risk is minimized. You peeing in the lake while swimming is more akin to the bush by the lakeside dropping leaves. However when it’s an entire town’s untreated sewage then it’s a whole other issue and the results can be catastrophic.

But yes 1 tonne of pure tensides is much worse than 1 ton of poop. However poop tends to come in humongous quantities which is where the real problem lies.

When it comes to toxicity to water life you have to think of the dose. If a rose bush sheds a few petals and it falls to a lake will anything bad happen to the life in the lake? No absolutely not. That happens naturally. The petals will quickly decompose and become nutrients that will feed the ecosystem in the lake. However if someone would drop a dozen truckloads of petals in the lake then that would be way too much organic matter for the ecosystem in the lake to handle. But some shower gel is never gonna come close to that. It’s more gonna be on the magnitude of the bush shedding some petals naturally in the lake. Same with the essential oil. Concentrated essential oil can be quite toxic to both human and other life. But in dilution it’s something else completely. A natural rose bush will evaporate tonnes of essential oil straight into the air during its whole life time and nothing takes damage from it. That’s why you can smell a rose plant when standing next to it. Dilution is sometimes actually the solution. A single drop of essential oil into the sewer drain once a day would not cause any negative effect at all when it’s diluted with tonnes of shower, toilet, sink and even industrial waste water. Diluted it won’t damage any life, especially since essential oils are biodegradable.

Also think what else gets down into the sewer. In most places your toilet and your shower are connected to the same system. The poop you put in your toilet is multiple magnitudes worse than anything you could use while showering. If your waste water treatment plant can’t even treat the poo then you have bigger problems then anything you could put into your shower gel. If it’s good enough to treat poo however then it’s good enough to treat whatever’s in your shower gel.