Image size optimisation is a good thing to do.
The output for web from Photoshop is very good, but you can get improvements through tinypng.com, particularly with png files as they know how to squeeze better compression out of that normally lossless format.
There is a bit of fiddly work in preparing images for web, but it's worth it in the long run. People do notice when a site is snappy and fast. It's a good thing.
Andrew