For sure, it'd be hilariously simple if your lightsaber crystal acts like a karmic mood ring:
Knight- "Master I'd like to study saber combat more extensively" Master- "sure my young apprentice, your blade is a brilliant blue I see no harm; in fact I saw this coming for some time"
3 years later after some rather risky missions
Knight- "Master why does the Council continue to order us on such tasks, it seems to endager us for less than positive outcomes. Many have been less than fortunate, and not returned with us" Master- "Be mindful of these doubts my friend, the council has it's reasons" *sees blade has been purple in hue for some time*
2 more years pass...
Knight- "Master stay with me, please get up. Don't die here Master!" Master- "Remember there is no...ugh"
Blade shifts hard RED...
Knight- "None of you will get away with this, I'm twice the swordsman he was. He simply wanted to take you in alive for questioning, I have no desire to do such a thing. None of you deserve to leave here if my Master cannot!"
...Oh that would be a little hardcore of an early warning system for sure! Watching blades shift during battles or after trauma. A little too on the nose for sure.
But to the initial part of if you're well suited to be a Jedi, well once you construct a lightsaber you're well down the path to becoming a Jedi. So if you just make one and BAM out comes a red blade... I mean yeah that'd be a hard pass on the rest of your training for sure. "Master what does this mean, nobody has this color?" "It means your training is at an end, and not in a good way."
I feel like the idea that you get assigned a color based on your role/path as a Jedi and then can later change it makes sense to me from an in-universe and a lore perspective. It also means I can head-canon that Mace Windu DID actually just decide he wanted a purple lightsaber because he's Mace mother****ing Windu.
I can picture it now, a skilled and confident young Mace Windu tells the Council that he has constructed a new lightsaber, and ignites a purple blade. I could see Yoda commenting "a purple blade you have. Represent Vaapad, it does. Channeling darkness and fury of both your opponent and you into a blade of Guardian blue to make purple you are. A wise decision this is, Master Windu." Mace nods his head and thanks the Grandmaster, but in his head just says "I just like purple you old mother****er."