Usually you don't get the entire sub-screen's data such that a blank versus null distinction wouldn't help. You can't "half submit" a dialog or sub-screen on the vast majority of systems I ever worked with it, and one adds time-stamps to critical sub-screens if they can.
Maybe you encountered a specific product's edge-case where it helps, but I'd rather trade away 9 other headaches to get your edge case headache. It may be the case that Product X doesn't allow time-stamps, but should we gum up all strings to make just Product X happy? I don't see how the tradeoff math favors that. Plus, it encourages bad designs by plugging problems with funny non-printable codes. Let's not enable slop-heads.
Re: but for other datatypes
For the purpose of this discussion I'm limiting it to strings, where the majority of null-related headaches are found in my experience.
I think you get it since you talk about time stamps. Just as you could record all mouse movements and keyboards to get higher fidelity you could break a single record into multiple with times stamps to record each step in a form, then the lack of record would be distinct from a record with all nulls along with time stamps. You could also do a record per field (which I have seen more than once) with metadata per field as other columns.
But without all that a system that supports null and some empty value gives you more fidelity than just null that again in my experience is practical.
Empty string and null work fine with strings for this purpose but for other datatypes you start needing to pick special values like the minimum value for a 32 bit int or 0 date etc.