The default mempool size is 300 MB. Transactions that were dropped can still be rebroadcast later. Nodes don’t usually go offline from having a full mempool, because the mempool limit is so small.

Either of the two may increase the minimum feerate for getting into the next block and price out less valuable transactions. Both filling the mempool or submitting a transaction with an inscription to the network are just ways to bid on blockspace. It seems to me that both Inscriptions and low-value transactions will be priced out in the long run, but while demand for blockspace is low, it follows that it’s cheap to acquire the undemanded blockspace. There isn’t much that one can do against it except to make more competitive bids for the blockspace.—If someone wants to make sure that the blockspace gets utilized fully, they just need to ensure that there is always another transaction bidding for blockspace at the minimum feerate.