I think Federer's problems in the GOAT argument are significant - Djokovic and Nadal have serious head to head advantages and also more slams and also more broad to head victories at critical moments. I don't understand the robotic comment as much as I understand that Fed can have a pretty looking game but there are no beauty points in tennis Moreover I find the athleticism displayed by any of the big 4 and Alcaraz as well to be incredibly impressive.
In any case, my main point still stands and it is not purely subjective but about how to handle significant changes in equipment and rules and surfaces across eras, changes that affect many players. It's not a trivial thing. That's why keeping the analysis within an era at least encourages the comparison of like with like. It's interesting that you like stats so much but are still willing to give the GOAT title to someone who largely dominated an era where he lacked competition, and largely stopped winning when his competitors came of age. How Federer lost that last Wimbledon final to Djokovic is still a puzzle.
It’s not that I like stats. I’m relatively indifferent towards them in the GOAT argument.
At the same time, you can’t simply dismiss them altogether. There may be caveats (longevity or play, competition in era, rule changes etc) that will impact the stats, but they will play a certain part in the argument.
Emotion plays a part as well, hence Federer rules the roost for me.
His achievements (whilst statistically not being the best), along with the way he approached the game on and off the court put him at the top of the tree for me.
But I’d 100% accept the argument for Djokovic as well - Just because I don’t like the player, doesn’t mean I can’t respect what he’s done in the sport.
I also love Nadal, but he falls behind Fed for me, despite (as you said) having better stats.
Unless there is a big reason (you mentioned Monica Seles for example), stats have to play their part in the GOAT conversation, otherwise it simply comes down to who your favourite player is.
That usually rules out newish players (Alcaraz for example), because he simply hasn’t had the longevity to be considered the GOAT yet.
With the Seles issues (where an exterior factor cut the career short), I think you can always mention them in the conversation, but very rarely (if ever) can they be considered the GOAT, again, due to longevity of career.
A lot of people have proved to be the best across a year or two in many different sports, but it’s the consistency that takes them from the best at that time, to GOAT status.