That part of it doesn't seem like the problem. If you want to make a carve out for some group and you're using a consumption tax then you just don't tax that thing or lower the rate (with the cost of having to increase the general rate on everything else). This is occasionally even a good thing, e.g. have a higher tax rate on petroleum than other things to price the externality, or a lower rate on groceries because they're a necessity.

And many of the carve outs are stupid and we shouldn't do them, but that's a separate layer of complexity/inefficiency on top of the mess we get from trying to pretend that "progressive marginal rate structure" and "means testing government benefits" are useful things to have at the same time when they're the mathematical inverse of one another, or that we want an "income tax" even though we don't want the major disincentive for anyone to have savings or make productive investments rather than immediately spending all income on hedonistic consumption.