Yes, I definitely meant priority. Highest priority transactions (transferring lots of old coins) get included in blocks first under the default block-filling rules.
And also notice that I said "most miners are..." There are at least a few big mining pools that have their own idiosyncratic ways of deciding which transactions get into blocks, including private deals with big exchanges/merchants/etc.
Also note that because finding blocks is a random process the Bitcoin network "stalls" for an hour every three weeks or so, with no blocks found.
My guess is that if an attacker tried to monopolize block space most of us wouldn't even notice. If you're really worried about it, then encourage some big mining pool(s) to have a completely different block-filling strategy ("randomly select from the memory pool" would be easy to implement).