I would like thoughts on a common spot I face where and hear input on whether they are false coolers or if they are indeed situations that I should just shrug off as bad luck and move on.

Effective stacks are 100bb (no reads).

MP limps

Hero (CO) Jc Jh opens to 4x

BTN 3bets to 12x

MP folds, Hero Calls.

Flop (26.50bb): 6s 3o 2s

Hero x/c 13bb

Turn (53bb): 4d

Hero x/c 25bb

River (103bb): 2c

Hero checks. Villain shoves. Hero calls. Villain shows AA

Is taking a check/call line on these types of boards with TT, JJ suicide? Am I better off just getting it in on Flop/Turn so the Ace-Kings can't play perfectly on the River?