This is just a generic checklist. Typically, hosts will give a toast. So, if you are hosting, you would give the toast. If your parents were hosting, they would. If your groom's parents were hosting, they would.
It's also customary in some places that the bride and groom give a toast at the wedding. But toasts are never required.
You don't HAVE to. The list that is on wedding wire or that you find online are just suggestions. You and your FH can give a toast at the rehearsal dinner to acknowledge and thank the wedding party. I'm sure they would appreciate hearing it from you guys. Again this is totally optional! But it is a nice gesture. I am not having a rehearsal dinner, but I do still plan on making a toast with my FH on the day of to at least thank everyone. We're having a small wedding. And it's totally up to you on who you want to give toasts. Just make sure that you give everyone a time limit lol. I say this because from previous weddings I have been to some people are more outspoken then others. So, they will talk your ear off if they get the chance lol! I know they mean well, but to keep things going it would be best to give a time limit. The only other people speaking at my wedding other than me and my FH are the matron of honor and best man. So, totally up to you!