Larger miners, Pools or super nodes will be able to afford broader limits on their filters and store more UXTO. As enough transactions get stored in the UXTO set eventually fee market will emerge, Some transactions are worth storing until they get confirmed while others are not and should drop out.
It depends what you mean by UTXOs "dropping out."
It is fine to do as you say and move UTXOs that aren't worth storing in expensive "hot" storage (RAM and the like) into cheaper colder storage (a hard disk). However, a full node
must be able to do an exhaustive search to determine whether a given UTXO exists or not. Otherwise, the node will be forked off the network.
It is fine if this "exhaustive search" takes longer for certain spammy UTXOs; in fact, it is actually a good thing because it slows the propagation of blocks that contain such spammy UTXOs down and thus increases the chance that the block is orphaned. This helps to create a fee market.