let's talk goals and context. think of equipment as tools just as lifts themselves are tools. say your goal was performance-oriented - to deadlift 500lbs in one year. in an extreme example, would you only do max effort singles for an entire year and disregard every other lift to do as assistance work? you'd be selling yourself short by limiting the number of tools you're using, and my argument is that the idea of "tools" is very relative when viewed in the context of someone's goals. for our 500lb deadlift, we would have an assortment of assistance work to help us get there. perhaps we'd be doing high-rep sets of dimel deadlifts to work our lockout - if our grip fatigues before the posterior chain, we'd be selling myself short by not strapping them. even if we're talking about the main lift and not assistance work, your main movement is still a tool and not always the end; its a means to the end of your ultimate goal. they might be one and the same depending on the timeframe, but its not an absolute thing. for example, when starting out our year, strapping our 2x5 deadlifts and training grip separately are a great way to ensure we maximize our performance in both regards. on the other hand, only doing strapped 2x5 deads for a main movement up til the day you're trying to pull 500 for a single without them is a bad idea. my point here is that equipment use is far too contextual for someone to come out and say "i dont use any equipment ever" unless that lifter is satisfied with selling themselves short. sorry to use you as an example TK, but you clearly have performance goals. "punishing yourself" by restricting the tools you have at your disposal isn't acting in line with what you want to achieve.
as far as non-performance goals or not caring how much weight is on the bar, there are a few problems with that. one, your goals are poorly defined and hence your training is at best directionless. two, as soon as you try try to clearly define a goal, performance invariably becomes involved and we come back to the nonsensical idea of arbitrarily deciding what tools you will and will not use based on something as asinine as "well one day i might not have straps so i should never strap up my deads." considering how relative the term "equipment" is, and if you even remotely care about the concept of progress, you are either a) short-sighted or b) okay with selling yourself short by not using equipment.