Snowie checks turn here because if I remember correctly it flats 100% of QQ combos preflop so this turn is very bad for your AK. But I would not follow Snowie and play exactly like you did but jam the river yourself for value to get called by many worse Ax.

There are not many bluffs you can induce on the river that prefer to bet rather than check back (like 2-3 combo of backdoor broadway combo draw). Qx float is always checking back its 2nd pair. So if you check river you are letting too many of those hands get a free showdown along with the weaker Ax you can get value from, so jam river yourself. This hand is just a cooler.

Checking river is very bad.
1. you lose a lot more $ than you make because you always xc when you're beat and never capitalize vs his worse hds. this is not even close to made up by his bluffs.
2. it messes up your 3 brl range terribly weighting you toward bluffs.
You let your opp off the hook and makes you easy to play against - the opposite of what you're going for