Developers have talked about wanting GW to test the depth of your bench. But personally, I don't feel that that's happening. As a mid-50s level player, I can usually take the same squad all the way through; rarely, across the last two or three battles I might lose one or two characters. (I realize, however, that at higher levels, the difficultly may become near impossible, which ought also be addressed.)
What if each character had some type of stamina meter that limited the number of GW battles they could do without "resting" on the bench?
Let's say that each character had several dots/pips/bars by their portrait on the squad selection screen in GW—let's just say 4 for the sake of discussion. Each battle fought depletes one of those. When they're all depleted, the character would have to sit out a battle (but could do so sooner for strategic reasons). Each battle sat out would replenish one dot/pip/bar. They could then go back out on the next battle or continue resting however long the player wanted.
Your non-A squad characters now have a meaningful and necessary role to fill: you could start with a B or even C squad when things are easier or when you need to rest up your best characters in preparation for the last battles.
If you're mid-level like me and GW is not too hard, your backup characters finally get used; if you're high-level, then they're not just frustrating, inferior replacements for when the battles are hardest and you're losing people.
More strategic thinking is required for when to use or rest your characters: having burned up stamina at the wrong time could cost you.
A possible disadvantage is that as it is, I have barely enough resources to keep my main squad leveled and geared; perhaps increasing the GW rewards could compensate for having to keep a larger stable of characters in fighting shape.
A much less drastic idea to encourage using more non-A squad characters might be allowing characters to recover more health when they're on the bench; that way, players might have more incentive to rest and heal a character earlier before outright die.
Lastly, I want to second a few ideas I've seen around: eliminate protection, add more opponent variety, don't predetermine rolls for each squad chosen. And from the sounds of what many higher-level players are saying, adjusting the difficultly might be necessary to make an idea like this workable for them.