Bitcoins can exist without exchanges, but would you support the argument that the existence of exchanges are among the factors facilitating the popularity and accessibility that people have to bitcoins?
I believe you're referring to the centralized exchange with this topic because you just saying exchange could mean both decentralized or centralized exchange. If you were not referring to any specific exchange but speaking on the fact that exchange in general has brought about a major contribution to the popularity of Bitcoin then that's accurate because without the exchanges there won't have been a means to exchange our assets to fiats or other cryptocurency.
The availability of exchange convince many investors to invest in Bitcoin because now they don't have to trust some unknown individual to send them there coins or money when they want to sell or buy Bitcoin. They can just trust the system which they're using to execute the trade successfully.
Main word you used is trust. And one of the main ideas of bitcoin is to make trustless financial system. So may be investors would better use a system where they see some exchange to trust, but they can use a classical financial system for investing as well. But trustless alternative is what returns a control over our money to us, what is important by itself. So there is a choice: to have entire control over own money in a trustless system or to trust a third party.