You compare pinball to foosball and billiards, but those are entirely different games with their own sets of rules. Of course nudging a pool table would be cheating, the game wasn't designed with that in mind. Pinball is. Somewhere along the line it became a crucial risk/reward element to the game, and anyone involved in designing pinball games in the past 50 years will tell you so. Some games even have playfield elements designed around nudging (Path of the Dead on LotR for example), or will reward you with extra tilt warnings (If it was cheating, and tilting only existed to prevent cheating, this would have never been a thing).

Pretty much every digital pinball game ever made also includes the ability to nudge. If it was cheating, the devs of pinball videogames would have the perfect solution to the problem by just not allowing it to be done, but they do because it's a mechanic, not a cheat.

In regards to pinball machines as art, yeah, they are, but they're also designed as coin-operated machines meant to withstand intense amounts of play and abuse at arcades, bars, etc. Giving it a push here and a slap there, especially in a home environment, isn't going to cause any noticeable damage. Your fingers resting on the artwork on the sides of the cabinet as you flip is likely to cause more wear than you will from slap saving.

Op, if you're unsure about nudging your games, I'd recommend getting Pinball FX 3 or The Pinball Arcade and messing with the nudging in those games. Should give you a good understanding of how nudging affects the ball and can be used to control it, and you can experiment without having to worry about damaging anything. Once you warm up to it digitally I think you'll warm up to it IRL pretty quickly.

You can have unpopular opinions no problem, there's a whole thread for that. Saying that you think nudging is cheating isn't an opinion, it's just flat out wrong. The rules of pinball are determined by the people who design the game. Stern, Jersey Jack, American, Spooky, etc. They have the authority to determine the rules on their games. Email these companies, contact the game designers, ask them if nudging is cheating or part of the game. They will all tell you that it's absolutely part of the game. If you still think it's cheating after this, then at that point you're just being stubborn with nothing to back up your argument.