Rings or MDF will create a solid mounting point around the whole speaker eliminating any flex. You are also stiffening the mounting area helping to eliminate vibrations into the door panels. A bad mount will make the best speaker sound dull, losing bass hit and tone. With a solid mount, you will get what you pay for.
I learned this one first hand, I installed my Heilx speakers in my Screw by just directly mounting them to the door panel and did some sound deadening. After reading advice here and DIYMA, I decided to give 3/4" MDF a try and was I glad I did. It made a very noticeable difference in the mids and gave it that extra "touch" to sound like a high end install.
As for negatives. If you have moisture issues, MDF will hold moisture but I know in my truck I never had those issues. You could use composite material, i.e., a cutting board if you are worried about moisture but I would be more concerned about protecting the speaker from moisture well before a ring.
FWIW, MDF is cheap and very easy to work with. I HIGHLY recommend using it.