Reach made a lot of questionable design decisions. I think the failure of its gameplay can be summarized by saying that it tried to be a spin-off, but was at the same time afraid to be too different from its predecessors. In many ways, I think they could’ve actually pulled it off better had they went full-on with the “normal soldier” gameplay that was popular at the time. However, instead they took the gameplay from Halo 3, and tried to add to that features popular at the time (recoil, loadouts, classes). There are two issues with that. The obvious one is that you’re messing with people’s expectations. If you just make a spin-off that bears no resemblance to the original, people just accept that it’s not meant to resemble anything they’ve ever experinced. On the other hand, if you try to pull a fast one by making something that looks familiar but isn’t, you will create expectations that you will not be able to meet.
The second issue is that not all mechanics are compatible with all gameplay styles. For example, recoil management in a game with already long kill times just can’t be a thing, because it massively lengthens the kill times. This can be seen in how bloom doesn’t actually behave like recoil in games such as Counter Strike where the shots start going all over the place very fast, and the whole reticle moves. So, if you can’t have recoil that actually requires control to hit anything at all, you’re going to end up with something that doesn’t require control, and in fact rewards spamming.
Armor abilities were whole another can of worms. Most of the problems with them are quite complex and specific to describe. Briefly, they failed at two levels. On one hand, they were either too shallow to have any meaningful use, or were completely detrimental as off-spawn abilities for competitive play. This is why (apart from bloom and loadouts, of course) Reach was met with a lot of distaste from the competitive community. On the other hand, some of the armor abilities also failed to resonate with casual players. Armor Lock is one that was pretty universally disliked, and I think had Bungie not made the mistake of including it, the game might have been a bit more accepted by casual players. It didn’t help that there was no effective way of telling which ability a player had until they used it, which meant that you really had no way of preparing for when the opponent was going to use their ability.
Beyond the additions made to the game, there are also various issues with changes to existing mechanics. The weapons were easier to use than in Halo 3, which again bothered competitive players. There was the lack of melee bleed through. Then there are the infamous paper vehicles that made BTB fans unhappy. The multiplayer maps were mostly mediocre and it didn’t help player perception that they also appeared in campaign, even if Bungie swore that they were designed primarily with multiplayer in mind. Invasion took some of the map design budget for itself, and so Invasion maps were repurposed for BTB, and bunch of the developer made maps ended up to be forged (which isn’t a problem from gameplay perspective, but people undoubtedly saw it as lack of attention).
In summary, Reach did some things wrong by either being too bold, or not being bold enough. On top of that, it also had a bunch of issues that had nothing to do with boldness. These latter issues are nothing unusual, and every Halo comes with them, but if the game has received more criticism than prior games, it’s because of the former drastic changes to the gameplay formula.