The only disadvantage is that it takes a bit more space. I personally think it is well worth it.
Before you go to far in changing your approach, do a search in the forum. You will find a lot of information on this subject - and how to make the change.
You need to follow a certain set of steps to make this work. Again, you will find the details by searching, but I will summarize my understanding.
1) Change your options to embed the cover art in the MP3 files (store images in tags also) - but this only effects new activity, it will not modify what already exists.
2) I beleive that you have to remove cover art from your existing MP3 files before you can proceed further - there is a reference in the tag showing the directory that has the cover art - this needs to be cleared out.
3) You can then do a quick find to update your MP3 files, which will embed the cover art in the files.
Make sure this is working correctly before you delete your cover art.
I actually keep the cover art stored in a directory plus embed the cover art in the files.