That's a legitimate option. It would mean that you could use the new, memorable domain name in advertising but send users to your established domain. But that means that would be the only advantage you'd derive from the new domain.
If this were a matter of branding, I could see the logic behind going the other way. If I had my site at thatguyssite.com, and I had the opportunity to buy qwertyssite.com, then moving to the new domain would make it easy to brand the site as Qwerty's Site -- much easier than just sticking logos up on That Guy's Site stating that it was Qwerty's Site, redirected or not. And certainly, having a foreign word in your domain name can put you at a disadvantage, unless the foreign word makes your site kind of exotic and aspirational. There's a big fashion site in the US with a French name, and here in America (and probably everywhere) fashion and French go hand in hand. This site is actually big enough that they run commercials on TV... in which they horribly mispronounce the French words in their name
I suppose if they pronounced it correctly, people would forget to type in that silent H.