Nothing stops anyone from using insps, but however, there was this corruptor in Siren's Call who popped alot of reds, a few purples and yellows. Then he went on rampage killing everyone on his path. He called himself a "good PvPer."(*)
I try to avoid using insps too much, and I expect the same for others. But if everyone else is using BFs while they're held, ok, I'll use some reds to speed up the kill.
Arena fights should always be done with full trays of insps. And then, I'm packed with BFs and lucks and yellows, in that order.
*) I hate people who use excessive amounts of insps in a short amount of time and when you use an occasional insp they start moaning how you used insps.
Personally I find people that only enter PvP zones with full trays of inspirations pretty cheap. I really don't like the mechanics in PvP zones, there is nothing that really limits the amount of inspirations you can get there apart from people getting too annoyed to get back and buy them.
I dont care if people use them, one used is one they no longer have and if they would sooner spend their time running back and forth to the shop then more fool them.
Making people pop BFs when I fear them is like a sub game to me 
**Acceptable "support" responses**
Its your fault
Its your computers fault
Its your ISPs fault
I turn off local and broadcast in pvp now as the utter rubbish people talk is just plian annoying. And it also make for a much more pleasant time as well. 
Insprinations! Divine insprination. Love em. They can help make up for shortfalls in a character, or just lend unpredictability, which is always always welcome to anyone who's in there for the fun of it.
I must admit, I feel a tad guilty when I buy a trayful of reds with my brute and two-shot regens, but hey - serves em right for not running away fast enough.
DON'T eat muffins while I'm developing you.
Pants! Turkey Magnates! A man in a box! Rogue AI! Come one, come all, to arc ID 10107 - It's [i]'Not as long as some other arcs'[/i]!
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like every1 says insps are there to be used, if ppl restock fair enough, its not exactly fair but when have the zones ever been fair?
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To to follow up on the restock question...
I find the downtime while end and health regen the perfect time to restock.