I'm not convinced that a London based franchise would necessarily be based in Spurs' new stadium. There's a deal there to play NFL games, sure, but there is still a continuing one in Wembley. Also, to make the biggest impact, you need to be at the biggest place. Wembley is not only the biggest but it's also the most iconic. Could be wrong, don't know the specifics of the deal with Spurs, but unless it's written in the deal I don't think it's a slam dunk.
Also, there certainly is merit to free agents not particularly wanting to be based in London. Especially whilst it gets going and isn't a winning team. However, you have to remember it depends on the logistics. Chances are there won't be a solo London franchise but instead a shared franchise. In that situation, the players would potentially only be based here for a month (assuming all London home games are played back to back). If they aren't back to back, they wouldn't be based here at all.
I think we are still a good few years away from a London franchise in the sense of an equivalent to what's in the US. We are likely to see a hybrid US-UK franchise first, which will essentially be one team playing multiple international series games here in a season.