I've been running a lot of pio simulations recently for single raised pots and have been noticing some weird trends in pio's solutions. I usually keep notes on anything conceptualize-able in Evernote and I've been noticing some "imbalances" in flop checkback ranges. I'll provide an example:

Flop Q95r, Btn vs BB, single raised pots.

Some Observations about how each range hits this board:
1. Btn has more overpairs/sets
2. About similar amount of two pairs/top pair/underpairs
3. Relatively symmetric in about everything else.

With a 50% pot bet, pio advocates betting with near 100% Frequency all sets, all two pairs, all overpairs, and about 1/2 of all top pairs. This is balanced by a high frequency of BDFD, weak Axs, SD's with emphasis on the BDFD, 1/3 of our 9x, and mixes for a lot of other hands. This is surprising to me. Why are we never checking behind our overpair+? When the flop goes x/x, we arrive on turns with a range slightly symmetric relative to BB's total range, except BB has more two pairs. This is a trend I keep noticing for many boards in SRPs where the preflop caller does not have too many overpairs/sets.

Further, in the line that goes flop x/b/c, turn x/x, our turn check back range also includes none of our sets/overpairs/two pairs. We literally arrive on river in the Btn with like 4combos of top pair, many combos of 9x, and a bunch of gutshots and Ax. When BB river probes (with an overwhelming amount of Qx, strong 9x, and missed gutshots), we are supposed to basically call with many pairs worse that 9x, and even a few combos of Ax. Is this something we are supposed to be going for? This doesn't seem like something I would willingly strive towards. Vs Villains that don't river probe missed draws, it seems like we should have to exploit fold our entire range. Has anyone else noticed something like this? Is not having nutted combos in our flop/turn check back ranges not very important?

EDIT: Also something I forgot to mention is that because we barrel flop with such a high FRQ of Ax BDSD or BDFD, on almost every brick river we can still have a raising range as we will always have trips/straights a low percentage of the time. However, our overall equity in the pot on rivers as BTN is super low.