The flaw in this logic is you'll only interest agents who care for exclusives, and they're going to ask for one anyway. Those who don't (and most don't), not only won't require/request an exclusive, but a whole lot of them are on record with their beliefs that exclusives are bad for writers and that they should be avoided whenever possible.
To those agents (and even to those less passionate about the subject, but who don't request them, nonetheless), I see two things happening: 1) You come across looking unsophisticated and uneducated about the process, and 2) You irritate the agents who've requested your work by attempting to barter a tight reading timeline for a perk they not only don't require, but don't want (and may abhor the very idea of).
As to your question, no. I want as many agents as possible reading my work at any given time. Offering un-requested exclusives ensures you'll only ever get one request. You and that agent could have serious differences in vision for your writing, communication preference, etc. But, you just had the one chance at an offer, so you'll either accept it, or turn it down without any other current prospects. For many, that's harder to do than it sounds.
Personally, even when I was in a position to, I wouldn't even grant an exclusive read to those who asked.