Risk vs Reward... Amulet of Health https://www.reddit.com/r/DnD/comments/dqdxkk/how_risky_is_dumping_con_on_a_warforged_paladin/ https://www.reddit.com/r/DnD/comments/mejemn/constitution_and_amulet_of_health/ https://www.reddit.com/r/dndnext/comments/avt41c/character_builds_using_an_amulet_of_health/ https://www.reddit.com/r/dndnext/comments/n0bm93/is_it_ever_optimal_to_dump_constitution/ https://www.reddit.com/r/DMAcademy/comments/nkokny/is_amulet_of_health_too_strong_of_an_item_to_give/

Amulet of Health
Your Constitution score is 19 while you wear this amulet. It has no effect on you if your Constitution is already 19 or higher without it.

Amulet of Health is largely a trap magic item. Outside of role-playing specific reasons, like playing a frail old man or a Toshinori Yagi (All Might) inspired character, Constitution is never a dump stat.

As a DM, if the player didn't specifically call out their reason for a low Constitution score and ask/expect an Amulet of Health -- they're probably not going to get it. Using the Standard Array, I can't think of any situation where I'd have less than 12 CON and the same goes for point buy, although I'd expect a minimum of 13 with point buy (and a plan to pick up Resilient at some point). I'd be skeptical of any player running less.

For players with legitimate reasons for an Amulet of Health, there's some value with setting your CON to 19 (+4 modifier) instead of using the expected +2 or +3 modifier but it's a rather expensive option. In many cases, Amulet of Health is going to provide the same benefit as the Tough feat (which isn't particularly strong in the first place).

Tough
Your hit point maximum increases by an amount equal to twice your level when you gain this feat. Whenever you gain a level thereafter, your hit point maximum increases by an additional 2 hit points.

This magic item is going to cost an attunement slot and possibly the only rare magic item your character comes across during the campaign. The attunement cost is slightly less for Artificers, but it's still taking away from a different magic item that could be attuned instead.

As far as improving your Constitution saving throw, gaining a proficiency bonus through your starting class or Resilient (CON) will almost immediately off-set the modifier bonus from Amulet of Health -- regardless of level. If you already have proficiency in Constitution saving throws, you'll get an extra one or two point bonus to it but is it worth the attunement slot? Probably not.

Cloak of Protection and/or Ring of Protection are better in almost any situation.

When is the Amulet of Health worth it?

Realistically, never. The two situations I can see Amulet of Health worthwhile is the following:

1. Fixing the drawback/role-playing aspect of a frail character (already mostly covered)
2. In settings where Constitution is constantly attacked.

The problem with the second point is that unlike other ability scores, like strength and intelligence, constitution is never damaged by monster abilities in 5th Edition. Wraiths, Specters, and Wights reduce a creature's maximum hit points, not their Constitution. Amulet of Health doesn't prevent reduction in hit points, so it won't stop instant death when/if maximum hit points are reduced to zero.

As an aside, Gauntlets of Ogre Power (including any variation of Belt of Giant Strength) and Headband of Intellect are much more valuable because they negate the Shadow's Strength Drain and the Intellect Devourer's Devour Intellect (as well as part of Feeblemind).