The only major improvement I can think of hosting images externally would be improving the overall speed of your website. If you run a pagespeed test with Google's free tool and notice your site is rendering slow then I would first consider reducing the number of javascript and css files being loaded. You will run into issues if your site is loading too many external files you can expect to see increases in bounce rates and poor engagement metrics. This may have changed but Moz did an expierement awhile back on if website speed impacts search ranking however if certain pages are taking too long to load they probably
This may have changed but Moz did an experiment awhile back on if website speed impacts search ranking. Even if speed does not directly impact rankings if certain pages are taking too long to load they probably won't be indexed.
What I would do is run Google's page speed tool on a few pages and if you have Google analytics on your site you can get some insights by looking at Behavior-> Site Speed-> Speed Suggestions and check out some of the recommendations Google is making about your site.If you have a problem with
If you find out that you have a problem with speed I came across a good article on some tips and suggestions that may be helpful for you about reducing http request.
I hope this helps some.