you will walk into a room and then wonder why you did so...

or wonder where you are and how you got there, etc.

Age does not easily prevent one from improving much or quickly or reaching (almost) one's principally possible maximum. Missing time and effort are the decisive factors.

I wouldn't want to become 1 Dan and stay there forever, for example.

Age does limit some of your abilities. As you get older - probably anything past about 30 - you will experience a decline in linear cognitive functioning, both go and non-go. You won't read as quickly, you will walk into a room and then wonder why you did so, etc.

There has been a certain amount of harping on how stupid old people are in some recent threads, but it's worth remembering that kids have a lot of free time. If you don't stop them, there are teenagers who will spend five hours a day playing video games, or talking on the phone, or watching television. If they set their minds to playing soccer, or drawing, or practicing the violin, they can get really good, really rapidly. If you're playing a game of Go a week, there is some go-happy 14 year-old out there who plays more Go in a week than you do in a year.

At the end of the 1 year period I will be stronger than the 7 year old, without question.

First: Why?

Second: The proposition isn't that the 7 year old will gain strength faster than the 30 year old, it's that the 7 year old will peak higher than the 30 year old in strength.

I agree with the Second statement, but I think that the primary reason is that the 7 year old will be able to devote much more time to go than the 30 year old. Most 7 years olds don't have children to take care of, or a living that needs to be earned.

I am 30 years old.

A hypothetical experiment: I am a complete novice at go and I am paired with a 7 year old complete novice. Both of us have one year to devote to studying go with no other life obligations or external considerations. We both study on similar routines with the same quality and volume of personalized instruction. I might not play as many games or complete as many tsumego as the 7 year old, but we devote the same amount of time to the two activities. (Perhaps I play longer games, or review more, or my approach to tsumego is different, or I choose to read a go book, or I'm just frankly slower.)

At the end of the 1 year period I will be stronger than the 7 year old, without question.

One of the key things a 7 year old lacks is the adult's or teenager's ability (but especially an adult's) to sacrifice now for reward later. Adults are able to put themselves through pain for several years for a cookie at the end, children find this kind of idea alien to them for quite a while. It's rare to find a kid under 8 who's able to do this very well. Some would put that age older. You need to force a young child to learn/practice/whatever (this could be quite subtly done but it's rather necessary with the vast majority of young children). You do to a fairly large extent need to take some of their childhood away from them. For a Western reference look at the training regimes forced on young children by parents wanting to give them a shot at professional classical musicianship. Or the training regime done by the Polgar sisters.

For every 7 year old working as hard as possible at go, or violin or chess there's an adult standing behind them encouraging/goading/whatever to make it happen.