Johnson has said that the whole point of the projection was to play on Kylo?s anger and thus impulsiveness, not just to have him appear as he remembers him. Kylo believed the saber was his, thus inciting even more anger at Luke for getting it back.
Additionally, as others have said, this version of Luke is ?Luke Skywalker?, the legend that everyone has created, and he has accepted that role, signaling that he made a mistake of throwing the saber away and running from his necessary role.
It's an odd overall idea anyway because Luke's face doesn't actually look any younger on Crait - the only real difference between Ach-to and Crait is the colored hair and beard. So the idea he should look younger in this HT figure isn't really true, it's really only about hair color.
The idea is doubly strange because the time difference between the hut scene and the Crait scene isn't all that long anyway - maybe 7-8 years. So the idea he should look noticeably younger on Crait to recapture that hut era is silly.
According to most sources, Kylo was 23 when he had the saber moment with Luke in the hut (though there does seem to have been some effort to make Driver look younger in the scene), and was around age 29/30 when Han was killed in TFA and the confrontation with Luke on Criat.
So I can sorta understand the choice of lightsaber to provoke Kylo (given how they parted, it's unclear why Luke would need to "provoke" Kylo,) but it's a very strange idea that to somehow provoke him Luke uses the force to color his hair - simply to recapture how he looked only 7 years earlier?
If the hut moment had happened when Kylo was 12 and he was now in his mid thirties (as Driver is) and this was recapturing how Luke looked 25 years earlier (Luke at a still-vital 40 vs Luke as a more noticeably older man at say 65,) I could understand it.