It's an interesting question you're raising. In many cases, the V.P. candidate gets chosen from among the other competitors for the party's nomination of a candidate for President who most helped the ultimate nominee to win the nomination (or at least caused him or her the least amount of damage). We saw the beginnings of this just after the South Carolina Democratic primary this year when Pete Buttigieg and Amy Klobuchar both dropped out and endorsed Joe Biden, as well as a couple days later after Super Tuesday when both Mike Bloomberg and Elizabeth Warren dropped out of the race. Clearly, all might be interested in considering a Vice-Presidential nomination at this point.
However, it's one thing to voice your support for another candidate in order to gain a leg up for the V.P. nomination. It's another thing entirely to actively support the candidate. I suspect in most cases that the nominee wants to actually see what the V.P. candidate brings to the table in terms of on-the-ground support, and they can only see that after watching how they perform in the rest of the primaries up until the convention.
Regarding picking candidates with home state advantage ... sure, home state advantage can be very helpful, but just because someone is from a particular state doesn't necessarily mean they'll bring that state's voters with them. For instance, Warren is from Massachusetts, yet she finished third in the Massachusetts primary on Super Tuesday this year behind both Biden and Sanders. In order to have a home state advantage, you also have to be able to bring victory in your home state.
Also, having a home state advantage isn't equally important in all states. For example, Bernie Sanders has a home state advantage in Vermont, but it's very unlikely that Vermont with its 3 electoral votes will be the difference maker in November. So if Biden wins the nomination, putting Sanders on the ticket due to his home state advantage in Vermont wouldn't be a good idea from the perspective of his home state advantage. He might or might not bring other benefits to the table, but home state advantage isn't one of them.
On the other hand, if the candidate in question were from a state likely to be a toss-up in the general election, such as Florida, Pennsylvania, Ohio, or Michigan, and that candidate had a good likelihood of being able to help deliver that state if named the V.P. candidate, then the home state advantage would definitely come into play.
Since this is more of a rarity than a commonplace event, home state advantage is usually not much of an advantage.