We don't even need a cure for cancer, we'll just not re-materialize the tumors. Brilliant!

Wil McCarthy's "The Queendom of Sol", very funny and entertaining series, recommended for whoever interested in that crazy idea (and a lot more):

https://www.goodreads.com/book/show/1361835.The_Collapsium

we could sequence someone's genes at 20 and just teleport you in your 20 year old self every time.

Man, can you imagine having to decide how you were going to look for the rest of your life (hair style, tattoos, piercings, musculature, body mass...) at age 20? It'd be like when you picked your AIM screen name at age 10 and then had to tell it to people in college.

[Minor nit: genes are insufficient to record someone's physical state.]

[Minor nit: I'd argue age 25-30 is probably a better physical peak to snapshot than age 20.]

You'd have to keep the brain intact if you actually want to keep existing continuously. That sounds trickier.

A lot centers around how you read the series to gauge the power of transporters. Bear in mind these are machines that A: Can accidentally leave a full copy of you behind (Riker) B: Can take your body and split it into "good" and "evil" halves, later recombining them (Kirk) C: Can combine two unrelated life forms together into one (Tuvix) and separate them later and the coup de grace for this discussion D: Can turn you into a childhood version of yourself that still has your full memories (Picard, Guinan, a few others)

So, canonically, the "beam yourself into a younger you" problem is all but solved. Yes, with various minor environmental pokes and prods, but meh, they've demonstrated the ability to replicate those when necessary, so hardly a stopper.

That last one is one of the most egregious examples of how weird it is that nobody ever follows up on anything that happens in Star Trek. Whoops! Figured out how to turn an old man into a ~14 year old with all his memories! Ha ha, life sure is weird, but otherwise uninteresting, right? Unimportant! Move on!

Is it "new life" or "new civilizations"? I think you will find it is not. Outside our mandate!