My DS, 11, loves DQ, and I also held it toward the end of the trip for the same reasons you mentioned.....I was afraid he'd never want to do anything else the rest of the trip. He's the kind of kid that could spend all day playing PlayStation, Nintendo DS, etc., and he did love DQ, but about a 1/2 day (e.g. 11 a.m. til 4 or 5 p.m.) was enough even for him. (It is very loud, etc., and you need to stand for most of the games...no lounging around on the floor like you'd do with PlayStation at home...so it can be rather tiring.)
We almost always go in June and have found that it's best to go at opening as it just gets more and more crowded from then. You also need to work against logic....e.g., go to DQ on a nice sunny day and go to parks on rainy days because most people do the opposite.
Last year we went as a family for the first couple hours, and then when the rest of us have had enough, we head out to DTD and leave DS for a couple more hours by himself.....we left him with both a 2-way radio and a cell phone, but neither of those worked very well inside there--either coverage was poor, or there was interference, or it was so noisy he didn't hear those when we called. Quite honestly, it did make me a nervous wreck. We told him to go towards the exit with the phone where it seemed to get better coverage if he needed to call us. He is very mature and responsible for his age....never gets in any kind of trouble...and he's also tall for his age, so he looks older than he really is. Additionally, there are lots of CMs around. On the other hand, arcades always bug me a little.....I always see grown men seemingly by themselves hanging around in there, and while most of them are probably genuinely there to play video games, with everything you hear in the news, it always makes me worried about what other motives could be. Anyway, I reluctantly left him; he was 100% fine; and other than me worrying a lot, it did seem to work out best for the family. Assuming your 14 year old is mature, trustworthy, etc., I think I'd be fine with leaving someone that age especially if I was still within walking distance and he had a way to reach me. I'll feel a little better if we do the same thing next year with our DS when he's 12 too. Logically, I do think it's probably safe....pretty big crowd so even restrooms are unlikely to be crowded and lots of CMs. It's just really hard to know when to let go!