That's a good point about the coinbase, I almost forgot about that. Does it actually have a purpose or can we get rid of that in this hypothetical?
You could get rid of it in this hypothetical. It doesn't serve a consensus purpose, but it does help to track who mines a block as miners usually will put some identifying text in the coinbase.
Conjecturing on we can, doesn't this make the bitcoin algorithm ASIC resistant?
Although you say that ASIC resistance is based on the hashing algorithm, I'd argue that the calculation of the merkle root is in itself a giant hashing function. If we use the merkle root as the only source of randomness, then I get the following calculations:
If we take the current hash rate of about 5,000,000 TH/s and multiply that by 10 minutes we get, 5,000,000,000,000,000*10*60 Hashes.
No, that is not ASIC resistance. ASIC resistance means that the PoW algorithm (in this case sha256d) is hard to implement on an ASIC. Merkle root calculations are also SHA256d; the data for calculating a merkle root can just be passed through the same SHA256d hashing chips on an ASIC. The processing that is required to do this is also very minimal and could be done on an FPGA before being sent to the chips to be hashed. I don't think the actual hashing chips themselves are even the ones that change the nonce. IIRC the onboard FPGA processes the header and then sends it to the hashing chips to actually be hashed. That FPGA would just need to process a little bit more to make the merkle root.
Which would mean that the number of different merkle roots we need can be calculated via log2(5,000,000,000,000,000*10*60) = 61.3796682. Meaning that each block would require at least 61 transactions for the miner to find a block.
We cannot rely on there always being some minimal number of transactions to be included into a block except for the coinbase transaction. While requiring a minimal number of transactions would solve several issues, I don't think that should be done as we need to consider the scenario where few transactions are being made. The network would grind to a halt if for some reason transactions are not being made (could be from Bitcoin falling out of use and becoming an even more niche thing, some layer 2 solution makes onchain transactions few and far between, some vulnerability is discovered that people stop making txs but the blockchain must go on, etc.).