That's a stumbling block for sure. I'd make it clear that you use Affinity primarily from the outset. And if they request Illustrator files that would be an added cost. However, if at the outset they want you to use Illustrator then you should of course use that.
End of the day, I just don't think it's worth the hassle of trying to persuading clients or companies about Affinity. No, harm in mentioning it and the money companies can save (assuming they have even upgraded to CC, as a lot of companies still use CS like myself). I also think it would take more than just one designer suggesting to make the switch for it to even really be considered. Designers are generally used to and comfortable working with Adobe, it is the industry standard, companies have it, so I can't imagine they'd care about saving the company money in order to support my suggestion.