I was thinking of Sims 2 when I answered, because I do play that more... in depth, and have a huge legacy family.
The only stage I "skip" is elder because by the time they get there, I've usually met their LTW, done what I wanted to do with them, and moved on to my next main Sim. I have a modded cake that allows them to peacefully meet their end after a few days of being an elder.
With Sims 4, I've tried to do the same thing. But I keep getting bored. So mostly I've played my young adult vampire Sim. She'll have a kid, maybe a grandkid, then I get bored. I build for a while, then I'll go back to her and start over. Sims 4 just doesn't seem to have "a point" with Sims and families like 2.
I guess I should have answered that I skip more than one, since it was about Sims 4. But I didn't think about it.
I played 3 similarly to 2. But I often shortened the lifespan of babies and elders in that one. (I don't play 3 anymore).