99% of terrible house rules are born from wanting to add "realism" or "logic" to necessary abstractions.
"I didn't design this with balance in mind" is most often said by people who either don't want to do the work to make something balanced or don't have to design chops to even try.
Tweeting at Game Designers, Demanding Answers
People who tweet increasingly aggressive questions to game designers--or worse, people who demand new content or rule changes under the guise of asking a question--are actively trying to tell you that they aren't well suited to a game that is essentially based on the premise "make up fun stuff."
The Bait and Switch
If you tell people that you're going to run an "old-school 5e game" but what you really mean is that you added the advantage/disadvantage mechanic to Swords & Wizardry, it kinda feels like you couldn't get any players for the game you really want to run and maybe you should think about why that's the case.
If you suspect that someone is cheating on their dice rolls, keep a tally of what they claim they're rolling. If the only roll they ever blow is for initiative, they're probably fudging and you can safely stop inviting them to your games.
The funny thing about cheating at D&D is that the stakes are so low. I get being attached to your character, but it's not like money is riding on how the roll goes--which makes me think that people who lie about their rolls are playing in your game for reasons unconnected from having fun with other people in a pro-social way.
I've never encountered anyone who lies about their rolls that isn't also bringing some other problems to the table.
Speaking of cheating, this Twitter post by Bluejay sums up why I never fudge rolls as a DM (unless I think I screwed up and added wrong, rolled too many dice in the heat of the moment, etc.):