Your proposal is to task congress with thousands of detailed decisions requiring deep and detailed knowledge of many areas. There is no way that could work better.
Congress turns over every two years. They can’t even authorize spending for the the things they have explicitly spent money on. Even if your congress person voted a specific way on a regulation what would it tell you? They would have thousands of such votes a year without enough information. The votes would quickly become bribe based.
An independent agency is simply an entity congress has created and authorized to interpret the details of legislation. Those interpretations are called regulations. They cannot just do whatever they want, there are many constraints. There is a process for making regs (including public comment). The interpretations are reviewable by courts. Congress can also address them.
This is definitely not a perfect system and I am sure there are better ones but it seems decent enough.
Nope. My proposal is that they must write the regulations or at least vote on them. You should be able to look at every single regulation and know whether your representative voted for it or against it. All regulation should be folded into the law and subject to vote.