Mysql datadir and binlogs: same partition or not?
For splitting a single physical drive into two partitions, I see only the big downside (as you pointed out):  You could run out of space on one partition, while having space left on the other.  (Many times I have seen this.)

For multiple drives, I recommend striping as being better than manually segregating this file/log/table/etc from that file/etc.  In many cases the actions are sequential (first scan the index, then reach into the data), making the manual split of no benefit.  And striping avoids the "out of space, but not really" problem.

Let's approach your question from a different angle...  Why give yourself more work (partition maintenance) when the benefit is questionable?

If you have one HDD and one SSD, then put the logs (sequential access) on the HDD and the data+indexes (random access) on SSD.