Other people may have responded to this by now (catching up on the thread after taking a break), but if not, could I respectfully (😉) suggest you (re?)-read the various direct replies posted in response to your original? They address so many of the above points.
It's a bit hypocritical then isn't it, to say that 13 year olds (who are at a similar disadvantage against adult men) should not be able to participate, or that they should not have a league of their own or be paid just as much for their international success... If we prize excellence above all else then why do we revere paralympians or women's teams?
Earlier posts address this with fairly detailed explanations as to why the female class/grouping is far from "arbitrary", and far more meaningful than those you hypothesise.
Alternatively, if what we prize is actually to do the best with whatever handicaps we start with, then why wouldn't we want a system that does a much more complete job of matching us up against similar opponents - or do what they do in horse racing. Add different fixed weights as a starting point in weightlifting for instance, then allow direct competition.
Earlier posts address this with representative facts and stats about male/female strength difference, including: 1) how males and females even of identical height and weight have massive differences in strength, 2) an allusion to 'the Phelps gambit' (google this phrase for detailed explanations - up to the point I've read, no none's gone into it in depth, and I'm rubbish at explaining it) and 3) the key observation that, if you're suggesting going by particular physical characteristics such as height, weight etc., these are themselves arbitrary measures as they're single variables selected from a virtual infinity of other directly relevant choices (eg. lung size, skeletal structure - and I'll add, to highlight this, bone density, q-angles, heart size, body fat, hormonal factors... etc. Which do you measure? How do you test for team membership? How do you organise for fairness. The least arbitrary way to do it is clearly to recognise that these all are determined (to a greater or lesser degree, and with inevitable outliers) by membership of one of two classes - male, or female.
I'm not actually advocating that we do these things. I am however (since this is apparently a discussion thread) trying to make people think about these things from first principles and see if they hold water.
I think you did - or, more accurately, a number of posters on shared brief summaries of conclusions they've drawn after, I suspect, many months and years of reading and reflection. Besides the science above, they responded with sociological, cultural and ethical arguments, and references to women's history.
I am finding it interesting that most people here seem to feel that privilege is acceptable without really engaging and justifying why.
This surprised me given what I've read, so did prompt me to post to highlight what you may have missed (fast-moving thread, I would understand!)
You could also google (I think Google's better as a search engine that the MN one alone) other MN Sex & Gender threads on this. There have been some fantastic ones, going into all of the arguments referenced by other posters and summarised by me above, in intricate detail with a lot of links to research and articles by sports scientists etc.