In general, targeting the people who literally don't care about price will not maximize profit. There are of course luxury brands that do target these people exclusively, but they aren't big companies.
Apple is a very strong brand so they can achieve high markups, but even they have price ceilings on what's reasonable, at least for their bread-and-butter products. Moreover, you can not just "decide" to be profitable like Apple by imitating its approach to product design and pricing.
That is not to say that you can't build a profitable company targeting the particular niche of users ready to spend $30/month for an email client. You just can't scale it.
LVMH’s market cap is north of 300B.
There’s plenty of scale in the price insensitive audience!
An attempt was made:
https://en.wikipedia.org/wiki/I_Am_Rich
> LVMH’s market cap is north of 300B. There’s plenty of scale in the price insensitive audience!
LVMH is a huge conglomerate of brands. I would argue that most of these brands are in fact not targeting the "price-insensitive" demographic, but those buying "premium goods", which isn't quite the same.
If you did a revenue breakdown, you'd probably see that the bulk doesn't come from Louis Vuitton purses, but rather from products that the middle class can afford - similar to Apple.