To each it's own but...
Look, I own an iPhone 8 plus and I will be splurging to get an iPhone 14 pro max.
Before you assume that I'm this Apple fanboi that feels the need to have always the greatest and bestest, lemme tell you about my history with iPhones:
My first smartphone ever was an iPhone 3G. My next one was an iPhone 5 ( yep, I didn't buy in the hype for 3Gs, 4 or 4s) . After my 5? An iPhone 8 Plus till present.
So nope, I'm no hipster that will feel inferior to everyone if I don't have the latest and greatest. It's not even a money issue... I'm not rich but I could have changed iPhones more frequently if I wanted, with a little bit of effort, no big deal.
Sure, I could do what the OP is gonna do an change of the battery of my 8 plus, it will definitely give a couple or more years of usage cuz as of now I basically need to carry a portable battery with me always.
However, if I do so, where I live, I would need to pay about 90-100 usd to change it. If I buy a new iPhone though, I can get around 130-140 usd cashback if I turn in my 8 plus. If I turn it in a couple of years instead, u get less of a cashback... by the looks of how much cashback u would get for an iPhone 6bow, my 8plus might get 30-40 usd IF lucky, or maybe even 0 money back.
Thus, on the economics of it alone, I SAVE MORE BY CHANGING MY PHONE NOW THAN TWO-THREE YEARS LATER. Not only cuz u need to factor in the money u spend on the new battery plus the diminishing cashback by turning in the phone, but also because inflation dictates that if an iPhone 14 Pro Max costs 1500 now, an equivalent iPhone 17 pro Max might cost 1700 then.
But let's leave the economics out of the equation and talk bout the REAL
reasons why I'm gonna change:
If I were to answer the same questions that the OP answered in its post, I actually would answer pretty much the same, but the problem is that my answers would be nuanced, there wouldn't be straight "Yes" or " No"... instead they would all be " Yes, but..." or " No, but..."
Let me illustrate this by giving specific examples on the three most important things (after phone calls and checking internet/emails/msgs, listening to music) that I use my phone for: taking photos, streaming and gaming.
Let's start with the least important one: Watching Netflix, Amazon Prime and Disney + on my iPhone. Look, most my streaming is done at home in my nice 4k Dolby Vision Atmos 65 inch OLED tv. More often than not though, during my long two-hour train commute I feel the itch to watch the latest episode of wahtever show I'm hooked up on... but I don't and it's not because of the screen SIZE of my 8 Plus... but because of the screen SPECS/QUALITY. Most streaming shows are Dolby Vision/HDR 10 ready, and once you're used to watching stuff with those vibrant and crisp colors and the moody cinematography they bring, you just can't go back. Those extra nits of luminosity a phone screen can or cannot output do matter to me. So can my 8 plus stream the same shows a 14 Pro Max would? Yes BUT its outdated LCD screen makes it that I wont enjoy them the same, to the point that I dont even wanna watch them on my 8 plus at all.
Gaming: Yes, my 8 plusstill can play the games I usually play. But as years have gone by, these games keep improving its visuals and adding things that require extra processing power. They are still playable but they run much clunkier than they did 5 years ago, even if playing them right under the air conditioner, at 100% battery and plugged in. A few of them are even borderline playable , actually. I can change the battery now but if things keep going as they are, said games might be flat out unplayable on my 8 plus in 2 or 3 years, or even before.
But now let's get into the MAIN reason why I feel I need to change the phone. I was so happy in 2016 when I got my 8 plus because it was the first phone that made me feel that I could skip carrying my nice DSLR camera and my collection of high-end lenses with me. Before, the iPhone 5 camera was for sure ahead of its time but it still didn't cut it. The 8 plus, never really matched the amount of headroom my DSLR set gave me in terms of post processing the pic, but it was "good enough" in terms of the compromise of not having to lug around my hefty photo equipment. Fast forward 6 years and this still remains true, but I have to admit that I still miss what my DSLR would get me if I would have carried it with me for that particular pic. I can't count how many borderline unsalvageable birthday cake candle blowing pics or other low light pics I've got, for example. This are the memories of my family, this is important stuff for me. The older you get , the more valuable these kind of things become. Not only that, the TIME you need to spend fixing the pic in post processing is also valuable. Dunno if the 14 pro max will get me this yearned DSLR quality, but if it get considerably nearer then its worth it. It would mean more headroom in post processing, and specially , LESS TIME sitting in front of a computer fixing that precious memory of mu family.
And here's where whomever is reading this would go : Ok, I get it, but you could get most of that with an 13 max, u dont need the 14 pro max! True.... if I would be the kind of person that is inclined to change iPhones every three years. But I am not, I hope to change it in at the minimum 6 years, so in the long run it makes sense to get the one with the better camera, better energy management, etc.
The OP and some other thread post also bring up the environmental concerns ... this attitude we humans have of wanting to change stuff even if what we have is perfectly usable. True, but correct me if I'm wrong ( and somebody please do confirm cuz what I'm about to write is one of the reasons why I stick with Apple) trading your old phone to Apple when getting a new one makes it so that Apple reuses wahtever can be reused from it ( rare earths, mostly I believe) and responsibly discards what cannot be salvaged. Of course, doing this just minimizes the problem, doesnt erase it but we do what we can, that is why I aim to change phones and computers at least 6 years apart.
So, in short:
TL;DR
The OP's logic is flawed in the sense that it is assuming a black and white attitude towards answering those questions.. and reality is rarely black or white, it rather tends to come in shades of grey.
The only valid "Yes" or "No" answer is the money related one: if you have an 8 plus and simply cannot afford a new phone cuz you have other important stuff to use money on, then of course the most sensible course of action is to change the battery, obviously.
But if money is less of an issue (specially because as I said,in certain scenarios , from the economic standpoint, if u do have the money it might make sense to change now than later) then all other questions are not hard yesses or nosses ( did i just make up a word?)... depending in your situation, they are shades of grey.
Having said this, for those of you who own 12 and 13 pro maxxes.... sorry to break it down to you but there's no way your shades of grey would tilt towards upgrading to 14 pro max ...unless you are a person that equalizes self-worth with having the latest and greatest.Consumerism as its best. 10, 10s, 11... I could understand.