I don't think it'll look stupid... I don't watch 90s sitcoms and think them using landlines, pagers and massive cell phones is stupid. Sometimes it's a little funny, but it's not stupid.

Literally ever show that's on at the moment that's set in the present day is going to fall victim to this, to a lesser or greater extent- why is Sherlock going to stand out on this? It's hardly a realistic show that's meant to portray typical 21st century life anyway.