Why are proteins made up of alpha amino acids and not beta amino acids? Or gamma amino acids? My idea on this would be that a world with beta or gamma amino acids would be too complicated? Is that true or are there other reasons?
Adding to Poutnik's useful answer, polyptides/proteins made of alpha-L-aminoacids are capable of participating in a number of secondary structures, such as alpha-helix, beta-pleated-sheet, &c. In turn these participate (along with the variety provided by aminoacid sidechains) in the construction of higher-order structural features with biochemical activity.
So one can say at least that things would be different if biochemical evolution had for some reason favoured beta or gamma aminoacids over alphas.
Also, as Poutnik suggested, the betas and gammas might more easily form unwanted cyclic lactams competing with any reaction (if still possible) to form (?pseudo)polypeptide chains. Then, even if such chains could still form in reasonable yield with beta and gamma aminoacids, the added methylene or dimethylene character of each aminoacide residue, (due to CaCb or CaCbCc carbon-chains taking the place of Ca), might restrict the overall range of physical-chemical properties in the pseudopolypeptide, irrespective of its side-chain -- perhaps, for example, it might make all aminoacid contributions more lipophilic than a corresponding alpha-amino-acid residue would do.
Really these considerations only add some approach towards exemplifying the difficulties of answer pointed out by poutnik. It may be doubted whether the subject holds enough urgency to persuade anybody to undertake the probably difficult course of synthetic and analytic chemical experimentation that would be needed to test the ideas.
Questions why? in context of various levels of life design are tricky and rather philosophical.
Beta/gamma amino acids would not be optically active, neither (alternative) proteins formed from them. As nucleic acids are optically active due present ribose/deoxyribose, there would be problem with their synthesis.
Aside of that, considering the length of eventual lactame (cyclical amid) cycle, 3-member cycle of alpha amino acids (as possible unwanted side reaction) is much harder to form than 4/5-member cycle of beta/gamma amino acids.