I know zip all about actual British English, which is a large part of why I'm utterly incapable of taking it seriously on a back-colony anime-haired JRPG protagonist.
I'll take a stab at explaining this. It might vary by person. For me, as a native English speaker who is minoring in Japanese, I find the Japanese less cheesy unless it's being done by certain recognizable and deliberately cheesy voice actors (such as Nobuyuki Hiyama and Norio Wakamoto). That's quite possibly just because I have a limited idea of what sounds "normal" in Japanese (for the longest time, I thought Hikaru Midorikawa, aka Marth, had a 'normal' Japanese voice. I was very wrong), and thus can't really decide something is cheesy unless it consists entirely of calling attacks (as Shulk's primarily would be) or accenting the -su of desu (which is... not nearly as normal as anime would have you think) or what have you. Furthermore, Japan as a whole has a greater... preference for silly or cheesy things. Just look at their ramen
commercials. There's a good reason many things can be reasonably explained as "It's from Japan".
Basically, at least in my mind, the original language is the one it's going to sound most natural in. And especially to those who set Xenoblade/Fire Emblem to Japanese and kept it that way, lacking a dub option is going to sound a lot like the character is being voiced "wrongly" for the first time (like Samus talking, which by most accounts was a terrible idea). The best way to fix that and cater to everyone is to simply keep both languages in. Doing so wouldn't even take up much extra space, compared to what else is there.