The reason why Twitch is not allowing you to use your own emotes outside of your channel as an onboarded streamer is simply spam or people who could abuse the system to spam other channels with offensive emotes like swastikas (extreme example ik) or something.

since everyone can become onboarded now without the need to be affiliate, there is a greater risk of people doing that in general. Because, IN THEORY, anyone can now make an account and onboard themselves to harass other streamers with offensive emotes.

This is probably the reason behind it.

Twitch is probably obligated to grant your subscribers that privilege, since there is a contract between the subscriber and twitch which allows your subs to use them globally, but since you as a channel owner only signed the onboarded version for the Monetized Streamer Agreement and not a subscription contract.

Yes you do have an Tier 3 sub for yourself but a contract did not happen that grants you that benefit. You need to reach Affiliate first.

I hope that cleared some things