I would find it really helpful if SE separate effects that can effectively scale in quantity indefinitely (like Dots) from effects that are binary either On or Off (like Debuffs).
I also have to disable other players' status effects on my target, because it's just too much squinting and clutter otherwise while I'm already trying to focus on everything else going on. But, as you say, then I miss out on important information like Virus/E4E uptime, TA, etc.
However, I would like to highlight one additional problem I experience: As WAR it is important for me to maintain Storm's Eye (sometimes also Path). During a hectic battle, sometimes Storm's Eye drops naturally (running from AOEs, etc), but other times I constantly reapply the effect — only to finally notice there's a NIN around.
The problem is that shared debuffs are filtered out by this setting, meaning that on my screen display, my important debuff has suddenly completely disappeared, so I assume it has fallen off. It's safer to just reapply it than risk it actually not being active, but this leads to a slowly-accumulating rotational inefficiency.
I encounter this issue as WAR and NIN (Storm's Eye vs. Dancing Edge), as MNK (Wait, I thought I just reapplied Dragon Kick — Oh, there's another MNK in this party), and DRG (Heavy Thrust → ... Wait, this should be a Full Thrust cycle, where did Disembowel go...? Oh, there's another DRG).
I think that Shared Debuffs should be exempt from debuff filtering (because these debuffs seem to automatically replace each other, meaning there should only ever be 1 instance of the icon on a Target display).
What I mean is, if I'm playing MNK for example, my Target should always display Dragon Kick if it's active, even if someone else applied it, because I need to know this information — it isn't clutter, the way seeing someone else's Touch of Death is (because I don't care about their dot uptime, it doesn't affect my rotation).