The only way I can see this working at all is if the graduating class (or at least the expected attendance) is very small, like under 30 people, and the attendees are all pretty close friends. The larger the party the harder BYOB is, even if it's a very casual BBQ-type affair. It seems like when there are more people (and sometimes when there are fewer) inevitably, someone ends up taking advantage of the variety of beverages available and drinks things they didn't bring. The only real way to combat this is to have everyone bring separate mini-coolers or boxes/bags with their own personal stuff in it, and then you have to find a place to put all these things, etc. It just seems like hurt feelings and rudeness waiting to happen.
Is this how your 10-year and 20-year were done? None of my reunions have been this way, but I was part of a larger graduating class from a private school and the expected party was something more formal - for my 20th there was a meet-and-greet on Friday, a golf tournament or a boat tour on Saturday, a dinner and dance at a hotel on Saturday night, and then a brunch on Sunday. If you wanted to participate in everything it was quite expensive - the meet and greet was $40 (included a live combo and passed hors d'oeuvres, bar was no-host) and the dinner/dance was $90, or you could purchase a dance-only ticket for $30 which got you in the door at 9 p.m. and helped cover the charge for the DJ. Again, the bar was no-host. My 30th is coming up and is already in the planning stages and it will likely be something similar this time around. I'd probably be thrown off by a change to BYOB for it and wonder what prompted the change.
If you determine that BYOB is appropriate for your group and it has worked successfully in the past for your reunions (so that the attendees are expecting it) then go for it, but do take into consideration how to keep people from thinking that the beverages are free-for-all just because they are all in the same cooler or fridge.