I run all my Rank 4s with Sol as my only healer, though I have Gaia in reserve also. Granted, I relied heavily on healing drops in my runs on Friday, and my other runs since the ATK debuff nerf have been Rank 3s (no cores).
Shingen seems like she'd work well in Thunder teams that already have a class A DEF debuff and Raiko. But if you miss the timing on the Burst, you're going to wipe (should be able to adjust that with ability damage). And if your DEF debuffs miss, you're in serious trouble.