Shooting yourself with a tipped arrow gives no effects in peaceful difficulty

Updated description by [Mod] GoldenHelmet
In peaceful difficulty, it is possible to give yourself status effects with the /effect command, but not with tipped arrows. This is inconsistent.

Steps to reproduce

1. Get a bow and a tipped arrow.
2. Set difficulty to peaceful.
3. Set gamemode to survival or adventure.
4. Shoot the tipped arrow straight up so that it hits you.

Expected result

You get the status effect from the tipped arrow.

Actual result

You do not get any status effect.

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Original summary
Shooting Yourself with a Tipped Arrow Gives No Effects
Original description
I am making a PvP map for me and my friends. One of the kits has you shooting yourself with tipped arrows to gain effects. It doesn't give you any effects with at least the following arrows. Jump boost, invisibility, water breathing, and swiftness