There would be a lot of knock on effects that would have large implications in encounter design. Off the top of my head:
1. this skews defensive CR valuation greatly. A low CR monster like a hobgoblin that trades high AC for low hp doesn't suffer very much from this change defensively (a shift from 11 to 5 hp means that most hits are one shots, but then, most already were) but their damage output become much greater. For monsters like hobgoblins, which are mobs, this is a net increase in danger level.
2. this skews offensive CR valuation greatly. A single big hit monster, like a giant, become capable of one shotting even higher level characters. Sure, these take a big hit defensively, but now even a mob of hill giants is something for mid-tier III characters to be concerned about.
These impacts need to be understood by both players and DM, the former so they can make informed risk decisions, the latter so they can present the level of risk they want. Overall, I think this add a lot to the swinginess of combat without commiserate gains -- 5e combats are already pretty fast and that would seem to be the major benefit of halving hp.
If, however, you goal is to create a game where combat is inadvisable in the extreme unless you can control the initiative, then this works well. I think that it would highly incentivize the "SWAT team" playstyle of recon and surprise and overwhelming force. It definitely de-incentivizes more reckless or "kick in the door" play.