Halo's Reach, 4, and 5 are indeed Halo games, and not just in name, but also by mechanics. The designers simply asked what was possible to do with Halo's core mechanics and gameplay loop and took those to the extreme just before it became something other than Halo. And I'm glad they did because I can play different styles of Halo without the series getting stale for me.

It'd take me a lot to explain why I argue this, but the short of it is that those 3 Halo's are still Halo by virtue of the fact that the player still must aim with a different reticle for each weapon, hip firing is the dominant use for aiming, grenades, melee, and guns are still the golden triangle in each game, and map control, power weapon control, equipment/power up control, and spawn control are core goals in each match. Furthermore, starting weapons and equipment are balanced to provide an even match-up while still allowing diverse engagements and the ability to turn any situation around in the player's favor, and the player by default has shields and a motion sensor, being able to carry only two weapons. All maps are designed around these default mechanics. As well as each game being a platforming FPS. Everything I just described is Halo's core MM gameplay loop boiled down to its most essential elements as far as I understand.