I read many posts and advice pieces that tell you to mix up your play. " You should check your strong hands sometimes so your opponents wont know if a check means weakness" or " Don't always check the flop when you whiff after a PF raise."

I seldom play with the same players. I'm lucky that there's a big player base here. I also don't know how many pay that much attention at this level (1-2) and 1-3. During the course of a single session, I don't see how mixing up your play has that much effect on your win rate.

At higher levels, and when you play vs the same player base, yes, I can see why that would be important. But at 1-2NL, I just don't see the advantage too often.

Straight-forward solid play better at 1-2 ?

1/2 you should be going for value like 98% of the time. bet when you have a hand almost always. players at this level don't really bluff, so checking for balance purposes is pointless.

the 2% of the time you can check when you have a hand is when you are playing with a maniac who you basically know, with a high degree of certainty, that they will bet. but if you are asking this question, you are probably to close to the beginning of your poker journey to accurately identify these spots, so just bet for value...

Yes

You can play a profitable game at 1/2 or 1/3 without balance or mix it up plays. Most such plays are sacrificing some immediate EV to make your play less obvious and gaining long term EV. If your opponents are not paying attention you don't need to.

The exception is c-betting when heads up. Situations where you have air after the flop heads up happen too often. Both c-betting 100% and c-betting 0% are obvious and even generally oblivious opponents will notice eventually.

i would say for an up and coming player, the 1st place to introduce a balance check is after cbetting the flop on a board that you actually hit and checking the turn. like you said, everyone knows about cbets. and people usually see people cbet flop, give up turn and if the V has enough ability, they will bluff the river as well as bet for value. on a board like J72 where we actually have a pair of Js, checking back a 3 turn can get a lot of bluffs on rivers when it's a low card because everyone will think you missed based on how all the other players play this spot