Yes, you should be able to select the class / spec you are going to play with. They could allow this in WoW.
Items could be either standardized since they are so much into templates anyway, or customized (ie, you can queue with either your specific alt or a standard-geared character provided by the system).
The only objective of "kill the enemy team" is fine, plus who says they can't add arena-sized BGs which do have other objectives? They were talking about that two years ago.
All of these problems with solo queue are imaginary. WoW arenas absolutely can be adopted for solo queues. If done right, that could make arenas immensely popular - hell, that could propel WoW back to its former glory and even surpass that. PVP sells.
The real roadblock here is that we are stuck with the PVP dev team who can't put even 1% of the required effort. All they could do is give content-free interviews from time to time about how they think it's "not so bad" or even good. That's it.