Removing EXIF data won't make your website faster lol. You should find other ways to achieve your goals ;)
Which is the case for listing pages of e-commerce sites, video sites, social networks etc.
As a frontend engineer, I find every way to achieve my goals as every ms matters :).
On a page with 100s of images removing the EXIF data from all the images would very likely have less of an impact than removing 1 image. Optimising is good, but you need to concentrate on optimising the right things. Start with the biggest impact and work downwards; chances are you'll never get to the point where stripping EXIF data makes a measurable difference.
Besides, if you're worried about every ms then you wouldn't implement a website that loads hundreds of images on to a single page in the first place.