I agree that iOS 7 was rushed. I know it would have been embarrassing for Apple if they couldn't deliver iOS 7 with the release of the 5s, but sometimes it's better to delay rather than releasing something half-baked. We would've all survived the Sept. 2013 release of 6.5 with a delayed 7.0 release. I just hope 8.0 is as stable as 6.0/5.0.
Software engineering is not that simple, sticking with older software on a brand new hardware wouldn't prevent this. Remember what we're talking about here, ARMv8 64-bit architecture was entirely new to iOS. Sticking to iOS 6.5 wouldn't prevent the crashes and memory leaks.
In addition, staying with 32-bit CPU and releasing iOS 7 would've been better but it wouldn't prevent the same thing from happening in iOS 8 when they do decide to release 64-bit devices.
Software optimization on a brand new hardware takes an enormous amount of engineering resources, both software and hardware teams have to be involved at the same time.
Heck, it took them 2 years (Mountain Lion and Mavericks) to get it caught up with the hardware in rMBPs. You should've seen the stuttering issues on Lion, horrific. Mavericks have finally resolved almost all of the issues there, especially with better performance on scaled resolutions.
The only true solution is to slow things down and not be pressured by the competition and sticking to the annual releases. However, this is difficult to do when you can't rely on beta teams with no 64-bit devices to test your software with.
Delaying iOS 7 would have delayed iPhone 5S, something that Apple can not risk with the 2 year contracts expiring from the iPhone 4+ owners. They need to get it out to get it in as many people as they can. The competition is very intense right now.
In fact, there were memory leaks in iOS 6 as well (think tabs reloading situation), it just wasn't as bad as the 64-bit type of leaks. It's worse because some of those 64-bit apps are using 30% more memory than before, assuming they're optimized for it. I know not all apps take up more memory but I'd imagine Safari does as Anandtech saw in their analysis.