One of the more seemingly legitimate criticisms of Monero is that the blockchain is susceptible to bloat due to its ring signatures. Are these criticisms valid, or do other coins have similar problems?
To some extent, it is, but it is also a common canard that FUDsters like to cling to.
Monero transactions are indeed larger than Bitcoin's, and RingCT transactions will be even larger. However, most of the data (signatures) can be dropped by a node after verification (there are drawbacks, though: this node can't serve a blockchain to another node later).
Besides, Ethereum's blockchain is now a lot larger than Monero's, despite being younger. The fact that there isn't such an outcry about the Ethereum blockchain size tells you a little about how real this "bloat problem" is.
Privacy isn't free. From what I understand, any coin that provides privacy will deal with at least some degree of bloat, as a private transaction will always add more data to the blockchain than a transparent one. This can be seen with coinjoin transactions in Bitcoin and Dash's implementation of coinjoin, both of which add significant amounts of bloat.
I don't think so as the increase in transaction size is proportional to the amount of privacy the user desires, IOW, if you want better privacy, you still need to pay for it. Any increase in transaction size will naturally increase the fees one will pay, and that miners are willing to accept.
There's no tragedy of the commons where people pay the same regardless of how bloated their transactions get, there will be a cost, and miners over time will become more and more discriminating of how big a transaction they are willing to include.
Additionally, miners are going to be less inclined to make bigger and bigger blocks after the block reward vanishes as the tail emission will provide a counter incentive to mine the big transactions. On top of that the POW algorithm will mean that CPU mining should stick around far longer, putting resource pressure on users that find the pressures of storing a balloning blockchain to be far less appealing than a big mining facillity in China.