City do need exposure, and no they have not got it yet. They still don't have the following that United, Inter or Arsenal have despite being successful and the other clubs being poor. Their fanbase is still small compared to these other clubs, and without these clubs there won't be much interest in them. The interest in the CL is largely because of the competition, but if that competition leaves a lot of the people will lose interest. This could be applied to any team, even us.
Also, they don't have any real attachment to the CL either to stick with them out of some loyalty. They don't want to quit the league and neither do the other teams,
Our owners and Arsenal don't care about competing for anything other than top 4, and that too because the CL gives more money. This SL thing basically guarantees them money every year, which is what they want.
The SL is not going to do anything special, but with most of the big teams with the most followers there that will get the attention. As for WC, for the neutrals it really is not that important as trophy. Not to mention a lot of the NT games are extremely dull compared to club football, which in itself can be quite boring as well. The CL is big because of these clubs, without which it will lose viewers and the same for PL. Football maybe massive for some, but for others their only interest is held by the teams they support and have no interest in the game beyond that.