It doesn't, the weekly chest provides up a choice from 3 items@226 ilvl from doing M+, and last I checked 226>213. M+ is at least on par with Mythic raiding in terms of loot rewarded on a weekly lockout, and well ahead of Heroic raiding. M+ is superior to normal raids, and for some slots it will still be on par with heroic raid gear due to itemization. Being 3 ilvls higher with your two worst stats versus a 210 item that has your two best stats, you're probably going to be using the lower ilvl item. Same with certain trinkets, the effects are going to far outweigh the mere 3 ilvl difference.
(Source of the numbers I'm using)
The only major difference is you can't spam M+ to match the ilvl of heroic raid gear, you're stuck like everyone else on the weekly lockout system for your best pieces. Welcome to the world of gearing that raiders always have had to face: Weekly lockouts, sorry that you're too impatient to deal with something that every raider has to cope with.
The upside is you can still get ahead of Heroic raiders in ilvl by decking yourself in 210 in every slot within a single week (I don't recommend doing it, but you will be able to if you desire). Heroic raiders cannot get a full set of 213 from a single week, it literally is impossible even if you get an item from every single boss and none of the items overlap on slots.
As to why I think raiding should reward better loot than M+: It requires logistical organization that far exceeds that of M+, and that effort shouldn't be discounted as having no value. The challenge of finding or organizing 4 people isn't remotely comparable to finding 10+ people, or arranging for 10+ people to meet the same schedule(depending on if you're pugging or doing organized raiding).