vanilla Call of Duty 1 (the expansion United Offensive doesn't count) and Call of Duty 2 (needs PAM Mod 2.04) were absolutely fantastic MP shooters, particularly for competitive. I have fond memories playing Call of Duty during the LAN party days in 2003-2004 and online in 2005, and while I was a bit late to the party, probably some of my fondest Call of Duty memories were during the late Call of Duty 2 online competitive scene in 2007 (Australia also had a revival of it in the early 2010s for a few years).
Both games had a high skill ceiling, and allowed for strategical and tactical skill expression as well as a variety of play styles being viable.
Both games had some flaws. CoD1 had some visual glitches with left-leaning and vertical axis that allowed for some problematic glitching to occur. Call of Duty 2 had a LoDBias bug that didn't correctly show foliage at a distance, making it unviable to play the map Brecourt competitively properly and also more imbalance in terms of viable weapons.
Weapon balance in Call of Duty 1 was probably the best, pretty much every gun was competitively viable - some more than others. In CoD2 there were certain guns that were just inviable for competitive - such as the M1A1 carbine (and CoD2 only Gewehr 43), which was not a popular gun in CoD1, but terrible in CoD2. The Bren in CoD1 was one of the best guns in the game, but absolutely terrible in CoD2 (same with the BAR), doing way less damage per shot than in the first game.
For instance, in CoD1 (similar to say Counter-Strike) every hit counts in that game, even a low damage tag from a stray automatic weapon spam from across the map can mean you are absolutely dead from the next proper hit, or not. It probably made the 5v5 S&D competitive mode more defensively-biased. The most supreme form of skill in the game was probably aiming with the non-telescopic bolt action rifles - the Kar98k, Lee Enfield and the Mosin Nagant. Machine gun fire (StG44, BAR and Bren) was often tap shoot for accuracy due to the high recoil. There are videos with one player with left alive with "one bit of bar" health (as health was not numbered) left performing 1vs5+defuse clutches without being hit. Probably from earlier in the online scene when people were less skilled (and internet was worse, haha). The Thompson SMG was also nerfed from 30 rounds to 20 per clip in Call of Duty 2. It was by far the most popular gun in the game, I would say. Definitely the easiest to use.
Call of Duty 2 introduced hit point regeneration and changed several game mechanics. In Call of Duty 1, when you jumped, you were unable to use your ironsight. It made jump shots not really much of a thing except at close range with automatic weapons, or in some cases close range 'shotgun' like shots with a bolt action rifle. Call of Duty 2 changed this and allowed ironsight to function while jumping. This really changed how the game was played. It made the game much more unrealistic, but also the change was very FUN. Now the most extreme example of skill was probably jumping off a roof, and getting a fully zoomed sniper rifle headshot in mid air (or, fully unzoomed, hahaha). Everyone is probably familiar with how ridiculous this became in the more modern modern warfare titles, so much so that it became a bit of a meme. One has to remember that was in an age of console Call of Duty with aim-assist, anti-lag network code and often in large public servers with dozens of players in the server. Performing the same shot in a 5v5 high level competitive search and destroy game on PC in the 2000s completely different.
Call of Duty 2 also had a shotgun, and Sniper Rifles also stayed zoomed after you shot, rather than unscoping while you cock the next bullet, like in CoD1. This made sniper rifles more powerful than in the previous game. There was also the introduction of smoke grenades ( a lay over from CoD1: UO). Competitive PAM S&D mode restricted teams to one sniper and one shotgun, and only the shotgunner was equipped with a smoke grenade, which lasted quite a while - can't remember for sure, maybe 30s - 45s in game time. The M1 garand was also a bit imbalanced, more powerful than it was in CoD1 - often a two shot kill gun. I think because of the existence of hit regeneration, a reduction in damage would have made the gun useless like the other lower damage guns (M1A1 Carbine, Bren, BAR, to some degree MP40). Shotgunning was an interesting skill - probably the hardest gun to be good at, despite it taking the lest 'aim' skill. It was a spread damage gun that fired several bullets at the same time at random points inside the crosshair. Due to how Call of Duty works (bullets are random inside the unscoped crosshair) sometimes you would have your sight on someone, and it would one shot them, other times, it would require two. It was easy enough to sit watching a doorway and shoot people coming through, but it took a lot of skill to be able to charge down an open street and get multiple kills without getting taken down.
A lot of the frag movies that existed were created before youtube, and back then casts of games were done audio only with a replay file provided for those that wanted to watch the shoutcaster's POV along with the cast. I do have one uploaded to my youtube. They don't even really give much of an example of the skill of the game other than the shooting part.
I only had the privilege of playing with BeasT a few times in Call of Duty 4 tournaments - twice at a LAN, and once in the State of Origin. BeasT was not as good at Call of Duty 4 as he was at Call of Duty 2, but even still, he was a top player. At every interstate LAN he attended, he would go out clubbing with the boyz, get absolutely smashed, rock up looking like shit, all red-eyed, probably still half-wasted and still perform at the LAN event. At the local ones, he usually dominated.