Why do we tie ourselves to a madhhab instead of just saying we're Muslim?

Bismillah. I've got a sincere question, and I'm asking it with respect because I honestly want to get it, not argue or anything. Why do we feel we gotta attach ourselves to a certain school of fiqh? I mean, do we really need to call ourselves Hanafi, Maliki, Shafi'i, or Hanbali? Why not just say we're Muslims and leave it at that? I seriously can't wrap my head around people saying all four Imams were right when they showed up many decades after our Prophet ﷺ. Like, how can all four be fully correct when they had different takes on some issues? One madhhab might say something's valid, another says it's not. Doesn't that look kind of contradictory? I'm not here to disrespect those Imams, may Allah have mercy on them. I get they were deep scholars and gave so much to Islamic knowledge. But my question is: why make a madhhab our main label? Why can't we just say, 'I'm a Muslim,' plain and simple? Same thing goes for tags like Sunni and Shia. Why do we split into different camps instead of just caring about truth where it's found? If there's something right in the Shia view, shouldn't we accept it? And if something's right in the Sunni view, shouldn't we take that too? And why don't more of us actually study our deen for ourselves? We spend years grinding to become doctors or engineers, but our faith is the biggest deal in our lives, right? So why not put real effort into understanding the Qur'an, the Prophet's ﷺ teachings, our history, and what the scholars left for us? Instead, a lot of us just follow a scholar, our family, community, or some imam without asking why or checking the evidence. Again, I'm only throwing out questions here. Not saying I've got answers. I genuinely want to get it: why can't we put being Muslim first, seek knowledge ourselves, respect the amazing scholars before us, and follow the truth wherever the evidence points? Wallahu a'lam.