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The reason footage like that exists is because that’s how the game originally released. But for anyone who played online Bungie eventually patched all that. Momentum or type of weapon didn’t matter it was still a 2 hit melee regardless.
This is incorrect. Yes there was a big title update to the game in
2005, however the game's beatdown mechanics and damage values are still momentum based. Unlike Halo 3, two standing melees do not kill an opponent in Halo 2. One of your beatdowns has to be running in order for that to work. UncutFighter has a great video on it that can be
viewed here.
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I'm probably in the minority that prefers the original starting weapons (SMG on H2, AR on H3, etc) on a lot of the smaller maps rather than BR starts on everything; but along similar lines as your comment, some of the games are completely changed and more or less spoiled by BR starts, particularly in H2C.
Example: The map "Midship" in original H2 was always such a glorious and refreshing change of pace because it was different. You had to get creative with duals/grenades/melees since everyone started with a plasma rifle, and a big part of the game was controlling the map and the power weapons with your team. Now it's just spawn and instantly shoot across the map with the BR, and the power weapons lose most of their value since a BR can easily take out a sword/shotgun unless it's close quarters. Simply put, it's a completely different game than that map was originally designed to be.
Suggestion for improvement would be to look at each map individually and determine what starting weapons make the most sense, instead of throwing a 'one size fits all' blanket over all maps. As stated in the quoted post above, BRs are 100% necessary on some maps, particularly the mid to large sized maps...but some of the smaller maps lose much of their fun with BR starts.
This is what happens when you don't have BR starts on small maps in H2. If you want to start your games with completely useless weapons, then I'd suggest sticking to Action Sack or custom games. AR/SMG starts are objectively terrible for players of all skill levels in classic Halo.