Is a store of value that requires a significant fraction of it be eaten up by transaction fees to maintain security going to be actually useful in the long term?

With regards to transaction fees, bitcoin is already not particularly useful today. It can make sense to be used as an alternative to wire transfers where you only occasionally send a transaction, but it isn't useful as a currency and any day to day transactions have to happen off chain and not use bitcoin at all.

Right, which is why one has to wonder who's going to want to pay enough transaction fees to secure the network.

transaction fees are not increasing though, so they can't offset miner rewards. they have been in the $100k-$200k per day range for a long time, with only occasional breakouts: https://www.blockchain.com/explorer/charts/transaction-fees-... and the trend is not to the upside. in fact with the arrival of ETFs in 2024 the trend is clearly downwards.

Making up a bigger fraction doesn't mean that transaction fees will increase over time.

For L1 fees to actually increase over time, we need increased L1 throughput. Without that, increased demand for transactions causes more batching of transactions (mostly between exchanges).

Given the failure of BCH for pseudo-religious reasons I don't have much hope.

But transaction fees reset to zero on each block. If relying solely on transaction fees, why would you mine if they are zero? So, on the start of each block, miners will shutdown, or perhaps switch to a different currency where it would be profitable to mine. This surely weakens the security of Bitcoin.

Rewards are also a permanent infinite money glitch that last in perpetuity? Or won't be changed in the future?

Rewards decrease due to halving and there is no guarantee that transaction fees will compensate it.