I actually think that transaction fees will be enough to support the miners without subsidy, because the miners will only process transactions with the highest fees.
This only works if mining is monopolized, with miners unable to compete with each other.
Otherwise, if Miner A will only accept a transaction if it carries an extremely high fee, then miner B will accept the transaction with a slightly lower but still high fee, and in turn miner C will process the transaction with an even lower (perhaps only moderately high) fee, and so on. The resulting bidding war will drive transactions fees back down to near marginal cost.
If you accept that mining is monopolized, then you don't have a decentralized system at all. But in that case, yes, you can indeed just charge transaction fees.
I don't believe a decentralized (non-monopolized) PoW system can be supported with transaction fees.