This makes me question, when considering overall gameplay, is it actually better to aim for an end state of a city
I am ALWAYS thinking about end state, for two reasons. The first is useless in the context of gameplay, as I am a bit of an aesthetic player, and I like to build 'beautiful' cities with a lot of features and optimizing certain things and even leaving a lot of unmodified hexes in between cities.
The second is that, yes, all the time hexes go unused between cities over the course of the game represents untapped yields (be it production, food, gold, etc.), but the utility of YOUR hexes towards the end of the game is also a function of the victory condition you are seeking. If I'm playing a domination or religious victory, then more important to me are my rivals' hexes, and how many of them I have 'occupied' by the end of the game. It doesn't matter if my own cities are small and have limited utility, as long as I'm pillaging or eliminating entire religions when I sweep across enemy territory I'm getting what I need to win. However, if I'm playing a science or cultural victory (dependent on yields in one case, and appeal or space for wonders on the other), then I'll need those cities to have expanded towards the end game. In particular, when playing a science victory, I will scope out 3-4 sites for large cities, usually including my capital, that I can max out production in for building the laser stations, and leave more open space for those relative to my others.
When I first started playing Civ 6, I always tried to max out city spread, so no less than 6 hexes between cities (every city got all three rings). I realized this was VERY suboptimal from a gameplay perspective, so I adjusted down to a default of 5 hexes in between (sharing the third ring), and now that I've been playing for over four years since the game came out, I'm actually down to a default spacing of 4 hexes in between (so basically every city gets two rings worth of hexes).
Another technical consideration? As Victoria said:
every move you make with a settler before settling is in itself less optimal before you consider the benefits of the target settle
So my question is, do you play on a small map on fast speed? Or do you play on a large or huge map on marathon speed? I play marathon, which means each turn I spend with a settler in transit costs me less time than it would on a standard or fast game.
The bottom line: it's all dependent. I will flex the spacing for each and every city based on my needs and where I want the city to be when I seek my victory condition.