I'm sure the team have ambitions on this like most projects no doubt do but it's likely at the start that they wont. These bigger exchanges charge an absolute fortune and it's just not practical for most.
You are right, most times is even best to start from a smaller platform and move to the bigger ones, reason that it has a kind of influence when a project move from small to big, the community will understand that they are serious but that aside, i usually say that big exchanges can't help a bad project, a project with a difference will stand out, no matter the avenue they choose as an exchange
I think the best approach is to use some not so famous exchanges at first time. Trading should begin from small volumes. And then when everybody is sure about reliability of token they can move to bigger exchanges.
It's most of the time also a question of the money a project wants to spend. Do they decide to spend a huge sum of the money they just raised to get listed on a major exchange to please all the 'moon-kiddies' or do they decide to go for smaller, cheaper exchanges, build up some trading volume there and increase the community so that maybe the community can help to get listed on Binance and co. by voting for example.
I think cross exchange at start is fine. But not all people like to have multiple exchange account for trading. So I personally feel that Bittwatt should list at one popular exchange.
In cases like this, I believe the best method to use is to create a poll for community members to vote and then the listing can be done according to the top voted exchanges in a descending other