In my experience, most people are trying to match a mixed and mastered recording. They choose the same amp used, but don’t think about the EQ used in the mix to fit with the band, the guitar used, pickups, other gear we don’t know about in the signal chain, cab, speakers and mics used, and most importantly, the guitarist’s technique and playing style.
I helped someone that uses a 0.35 mm pick and couldn’t match the percussive attack of a recording. They tried to get it out of the amp block. I asked if they had a thicker pick, they did, and it was instantly what they wanted.
It’s not always the amp.
Like you say, it's a finished product that many try to replicate. It's practically impossible to get it dead on most always, and that isn't really the fault of our gear - no-matter how good that gear is. It's Their Gear, "they", in general, that we don't have access to, which cause the headaches.
Another thing too.. Ear-fatigue.. For me, that's a real thing. These days, generally, I just get it close - ballpark - even when I know it's not close enough. Get it ballpark today, tomorrow I am better able to fine-tune. Too-long spent tweaking in a single sitting - for me - the next day I found that whatever I was working on sounds awful after a decent break.
I learned long-ago that although the day before a marathon tweaking session I might have convinced myself I was getting nearer the goal-posts, in another sitting, I found that - for all that work - I ended up with a preset much worse than I initially and very-quickly dialed in that day before.
These days, for me, as long as the amp sounds close with the grit or chime, I can dial the majority of the rest of the way in with a cab selection. Everything outside that is so much easier to dial in afterwards.
A person can always Google amp/cab/speaker/effects setups before they begin, too. Oftentimes that information is out there, and - with a good modeler - it will get a person in the right ballpark where they want to be pretty-much immediately.
Main thing - I found - is to be realistic about what you are trying to achieve. Like you say - it's a culmination of all aspects of That sound that you are trying to replicate. And - even if you could replicate talent and style - which we can't - there is a lot in that finished product - that closed-loop that we just don't have access to.
After decades of screwing around with these types of high-tech things - for me - I keep it as simple as I can. If it sounds good, it's close enough. And it will likely sound close enough to anyone listening, too.
I'm done being the perfectionist. Too much of my time wasted on such a silly pursuit. :0) ..It used to bother me, back in the day, when, after a show, somebody occasionally told me I didn't sound exactly like "that guy".. Today? ... Well, there's a reason for that. I ain't THAT guy! This realization has saved me all manner of sleepless nights. :0)
Anyway.. each to his own and all that. But, for me, close enough is close enough.