I really doubt this lends much to your argument, first of all because I think it's highly improbable any player regularly gets C5 out of the gates early on any high level game, and secondly because I play high level games all the time. It's more of an anecdote, and doesn't really represent gameplay. What you really see is the tedium of C1 & CII versus CRI and CRII, and things like siege unit promotions being especially pointless after the siege unit changes since vanilla. Promotions are just tedious - if it weren't for the traits relating to them and rather abusable things like using promotions to heal a lot extra, they add very little even to a human player's game.
If you're presuming somebody you have an empire ahead in tech, already conquered everyone else, etc... then of course you could be expected to win, but promotions don't really help with that. The difference between regular units and promoted units is very neglible in most games, and when you do get promotions, it tends to be applied everywhere, nothing making units very unique besides the occasional Medic 3 General.
You need 2 Battleships or 1 Battleship and one Bomber to kill that. In fact, that was an example I already used in my post - getting promotions on naval units takes ridiculous amounts of time for very little benefit. After all the work it takes to upgrade old troops to CRIII Rifles, they can just be beaten by regular rifles and cannons anyway. You probably are assuming tech and other advantages everywhere you go - promotions give a little extra push towards domination when already in the lead, but they don't really matter that much.
And one other response:
I didn't say and wouldn't necessarily be out to argue this is a majority of total people playing the game. In fact, I hope it's quite the opposite, which is why I think the developers really should heed such calls to avoid single-minded focuses. However, it is a large proportion of people arguing in threads like these though, so I welcome it if you have the time to read over tons of posts for yourself. Part of the problem is a large number of people never express opinions on different issues - if all they ever do is pop in to comment on one thing about war, you don't really know what they are after, but what they say is often along those lines.
See, the thing is, I really do not think that is the case. It's rather self-evident from player consensus, for one - if promotions were too powerful, Aggressive would commonly be rated as the very top trait, and routinely it is rated rather in the dumps. Promotions combined with technological and other advantages led to snowball effects - I think Sonoreal rightly pointed out how this works. But they usually are far less effective than defensive positions, collateral damage and other factors turn out to be. I think players would be hard pressed to find a time when a single but highly promoted unit on flat land could take on armies. The AI having a CGIII unit in a city on a hill with a castle may have stymied a lot of attacks - but when you look at it the promotions aren't even a majority of the bonuses to strength, and enough catas still take down the city.
On their own, especially without certain abuses (eg. healing) they matter too little for the effort, especially past the first couple of tiers. Managing to get 5 XP/2 promotions instead of 0 is fine, but at the same time everyone can do it, and then that civ's troops are hardly much different in effect from somebody with 5 Great Generals settled down somewhere and 17 XP on their troops.
I will stress though that as I said, I favor making promotions more rare and thus unique in return for making individual promotions stronger. Civ4's system just can't be said to be that overbearing and is often tedious, which was the problem.
If you make promotions more rare but more powerful, you are just turning civ into a tactical tile *cough* I mean hex based game. Those games already exist. Civilization is a game on a strategic scale. Individual unit uniqueness shouldn't exist. The differences in strength (and role) is already represented by there being different types of units (legions, catapults, tanks).
I have earlier though, it would make sense for one military to be more well equipped or supplied, or trained than another. This could take the form of military wide promotions (as opposed to individual unit promotions), which would give you an edge against a less prepared foe.