Well, the old games didn't tell you much who you were, but you knew. You knew if you were the kind of practical type that would have Jan drink a few potions and then sell a few suits of full plate, then pickpocket those suits of full plate, then sell another couple of suits of full plate that you had recently, ahem, acquired. Or maybe you were too lawful and wouldn't even cheat a shady merchant that traded in stolen goods like that. You would know if you got the youths into trouble with swords and alcohol.
But you were just very limited. As I said: you could tell yourself that this is what you did with the mechanics. But even the dialgue possibilities with just the tag system are streets ahead today. In the old games you mostly had Answers 1,2,3,4 and they did not change much if you were another race, class or had some proficiency.
Things like class tags in the dialogue can used to put a bit more emphasis on precisely who and what you are, but I feel that all the skill check rolling BS is actually detracting a fair bit. Suppose you have shitty rolls, does that mean you ought to never learn anything about your companions? That they never open up? That doesn't feel right. Suppose you have rubbish skills for the check but extreme luck with the rolls (or you savescum), what does that mean, then?
Most dialogue with the companions is more choice based, than CHA-roll based. But yeah, if your uncharismatic barbarian has more muscle than charme, you will be more often in situations where you cannot sweettalk your way out. But on the other hand you also could be the suprisingly charismatic barbarian, who has other flaws.
The roll system is a fundamental part of DnD, so yeah: sometimes things will work out, and sometimes you are unlucky. This is just that extra bit of chaos that makes every encounter a little more individual. Sometimes something even works out if you are not a pro at it. Also remember: a lot of checks do require you to be at least proficient with the associated skill, just to let you roll. So its not the cliche of "i am a dumd barbarian, but I got a nat20 so I understand those arcana runes, even tho i am not proficient". Otherwise: its a singleplayer game mostly. People can just cheat or scum if they really want. I dont see the point of working around that.