Tofu. Problem solved.
I suppose that in countries where soy is an important crop, tofu may have a competitive price, but not here.
For a sedentary life style it is impossible to compose a vegan diet that has enough proteins without containing too much energy.
It is necessary to use at least one protein source where a special method has been used to separate the proteins from the rest of the vegetable.
There are plenty of such products on the market, like tofu and various protein extracts, but all of them are much more expensive than chicken meat. At the tofu price mentioned by another poster it is 2.5 times more expensive than chicken breast, while other kinds of protein extracts that I have seen around are 5 times more expensive than chicken breast.
The discussion was strictly about how to get vegan proteins cheaper than meat. When you are willing to pay many times more than for meat, then of course it is trivial to eat a vegan diet.
Because all commercial products are more expensive than meat, the only other way is to extract vegetable protein at home. I am aware of only a single source of vegetable proteins where the proteins can be separated without any special equipment or chemicals (excluding soy, which is expensive in Europe), and that is wheat flour, from which the gluten can be separated from starch by simple washing.
But in any case, even paying double meat price for tofu protein, $.05/g of protein, is still "too cheap to meter" in the context of an industrialized lifestyle.
They are necessary for a vegan diet, but they are not sufficient. They must be combined with some other source of proteins, which must contain much methionine and which must have a better ratio between protein content and calories.
The commercial protein extracts from them are much more expensive than meat, so they are a non-solution.
Using so much energy requires many hours of intense physical activity. When your job requires spending 8 hours or more per day sitting in front of a computer, then it is absolutely impossible to also do enough physical work to consume over 3000 kcal.
Therefore your suggestion is also a non-solution for many people.
It is true however that for most of our ancestors the problem of gaining weight when eating a strictly vegan diet would not have existed. This is indeed just a modern problem, of the sedentary people.
For instance, bread is normally considered to be an incomplete source of proteins, but that is just because one cannot eat enough. Eating bread made from 1 kilogram of flour per day provides enough of all essential amino-acids. It also provides about 3500 kcal/day. Someone doing hard physical work, like it was much more common in the past, could eat only bread without needing any other source of proteins.
Lentils have 26g of protein and 353 calories per 100g, and eggs have 13g of protein and 143 calories per 100g, so the ratio is 13.5 for lentils and 11 for eggs.
Doesn't seem all that different.
On the other hand, lean meat is almost pure protein, so its ratio of protein vs. energy is 3 to 4 times better than for vegetable sources.
Even with whole eggs, you can get much less calories than with lentils, if they are used to supplement cereal proteins, because they have a significantly better lysine to calories ratio, so when the amount of required lysine is specified you can eat less of them than in the case when their amount would be computed to provide a specified amount of protein.