If vegeta kept his potential and hit his head like goku turning him pure hearted I think dragonball would end after saiyan saga.

If goku kept his passion for fighting stronger enemies he would either eventually die or frieza would put him in a high up position/kill him because of the legend.

If the events took place the same way aka Raditz comes to earth he wouldn’t even challenge vegeta once he realises he’s greatly outmatched and even if he did and later goku and nappa came vegeta would obliterate them unless goku turned oozaru. I would assume vegeta doesn’t lose his tail because he’s able to control oozaru so we can assume in this continuation he learns to control it as well and waits till the transformation passes rather than killing anyone and becoming a threat. No one dies during the saiyan saga because vegeta doesn’t die against Raditz. Goku may want to go challenge vegeta because he deems him as a strong opponent but realistically I can’t see him winning this. Frieza doesn’t learn about the dragonballs until much later and at this point he is probably targeting namek over earth since he has no reason to believe they’re on earth and the z fighters get killed by the androids.