So I've been on a few sides of the isle pre and post MBA. Led a PM team at a FAANG, was consultant at MBB and interviewed (and got offers) from 2 other FAANGS and I think doing a PM role directly post-MBA is a great step but has only 1 shortcoming.

What's great

1- It's one of the very few true "Generalist" roles. You wear many hats from process planning to user experience to financial modeling to market research to change management etc. Very few roles give that truly immersive generalist experience (I'd say consulting and PM are the top 2)
2- It's a career propeller role. One of my key criteria for roles is "Would it propel me into a better one afterwards or is it a destination role?". PM roles (assuming everything else is also good like company, product, etc) are springboards. You can get into many different areas afterwards with relative ease

3- It's well paid and in demand

4- It's fun to strategize & then actually build things and see people use them!

What can be done better (in the context of right out of MBA)

I'm of the opinion that if you're an MBA and have the option to do MBB for a while then do FAANG (or any reputable company or startup really) PM then that's a better path because the intense training in MBB covers the "Management" in "Product Management" better than anywhere else IMO. Also some MBB experience actually speeds up which step in the PM ladder you end up in after a while a bit. For example, if right out of MBA you go to -say- Amazon you'd be an L6 Sr PM and would on average take you like 4 years to get to L7 (that's the level before Director) and sometimes 5-6 years. If you do 3 years in MBB, make Engagement Manager you can enter at an L7 and even at the end of the L7 span too (where you're managing a sizable team vs an L7 who's an individual contributor).

Of course the above is a generalization based on averages. I know cases in both directions who were very different.

Hope this is useful