At some level, it doesn't make a big difference if you've got a file open or not once the file's data falls out of the disk cache, you'll have the same kinds of latency to get it back. Sure, you'll avoid a round or two of latency pulling in the filesystem data to get to the file, but probably not a big deal on SSD.
Chances are, the popular databases stay in cache and are quick to open anyway; and the unpopular ones are rarely accessed so delay is ok. But you'd also be able to monitor for disk activity/latency on a system level and add more disks if you need more throughput; possibly disks attached to other machines, if you also need more cpu/ram to go with it. Should be relatively simple to partition the low use databases, because they're low use.
Chances are, the popular databases stay in cache and are quick to open anyway; and the unpopular ones are rarely accessed so delay is ok. But you'd also be able to monitor for disk activity/latency on a system level and add more disks if you need more throughput; possibly disks attached to other machines, if you also need more cpu/ram to go with it. Should be relatively simple to partition the low use databases, because they're low use.