Afaik:

Yes, in the long term, cutting T from body will reduce hairs, and everything, You may be dead on that! OR at least very very very sick on many levels.

Our bodies NEEDS some T and optional E hormones to work, not only for body hairs, but pretty much everything. Yes, girls, both cis and trans needs a little of androgens too! That's why getting correct dose of blockers is so important.

If You feel to be too manly on some aspects, it may be worthy checking if You do not overproduce T naturally, that would be bad too, then ask doctor for small dose of blocker, to put the level into desired amount. No less, doubt that would help much against facial hairs.