Hi,
As Dave points out, there is no competition between higher plants and algae because they have totally different requirements. So it really doesn't matter what level of nutrients in in the water, low or high. We can see this demonstrated in tanks all over the world. However, yes, it is a good idea to have a sufficient mass of plants. Again, this is the problem with interpretation of the facts. No mass of plants can possibly compete with algae. This is not what plant mass does. Plant mass supports the symbiotic relationship between themselves and the bacterial colonies. If anything, it's the bacteria who do the competing. Having said that though, healthy plants do uptake ammonia, whose production rate is one of the triggers of algal blooms. A high plant mass is better able to attenuate the ammonia production rate and this is very useful in new tank setups, since the ammonia production rate is high due to a lack of established nitrifying bacterial colonies. There is a direct relationship between the stability of a tank and the stability (type and amount) of the bacterial populations. The symbiosis between plants and bacteria is the key simply because rooted plants support the bacteria.
Now, I don't doubt that this can be accomplished with floating plants alone, but since there is no contact with the sediment and the floating plants they cannot possibly be as effective with regard to the sediment bacteria. The oxygenation rate of the sediment cannot be as high without root interface. Rooted plants send oxygen from leaf to roots which escapes into the sediment thus oxygenating the sediment and supporting a higher nitrifying bacterial population in the sediment. These bacteria then make nutrients available to the plant roots. Without this interface the probability of oxygen starvation in the sediment is much higher which leads to a higher probability of stagnation because when there is low oxygen content in the sediment other bacteria arise which convert ammonia via other elements such as sulphur. So instead of nitrate or nitrogen gas being produced, there is a greater likelihood of noxious compounds such as Hydrogen Sulphide being produced in the sediment. While floating plants do contribute by ammonia uptake, the oxygenation is limited to the water column alone which can only find it's way to marginal sediment layer.
So I not saying that an exclusively floating plant tank is doomed to failure, far from it, only that it's a different environment with different dynamics, specifically as a result of the lack of root/sediment interface. So the hypothesis that somehow this would be an alternative configuration in case some other configuration fails is murky because one can fail (or succeed) using either. One would simply fail or succeed for different reasons. I'm not sure how you're defining "failure", so other than algal blooms it's not clear what other failure modes you have in mind. In any case floating plants have a superior advantage over their submerged cousins in that they have full access to atmospheric CO2, which makes them almost bulletproof, almost to the point of being a nuisance. I have yet to see an interesting duckweed show tank, that's for sure.
I regret that I can't really give any ratios or quantities in terms of floating-to-rooted. It doesn't work that way. It depends on the amount of light, the nutrient scheme, the stocking levels - and an important factor is aesthetics. One needs to define their goal. What does one want the tank to look like? To me that's the first question to answer. Then, design the other factors around that to make it work.
As regards the necessity of a filter, as D. Walstead has demonstrated, no it's not necessary. I guess the question is "What are the objectives?" Without a set of well defined objectives, configuring a tank in a certain way may be either pointless or fraught with pitfalls. Are you wanting to configure the tank in the Walstead scheme, because that's the way she did it, or did you have your own set of imperatives? Do you want to illuminate the tank with sunlight only, for example? I just think that we each live in our own different world and that it's great to use ideas from others to construct that world to make it prettier or easier, but the ideas have to work for us. Certainly, having a filter is easier than not having a filter, and having rooted plants has better long term implications than not having rooted plants, but either method can work.
😀
Cheers,