No it shouldn't. It should be a listed building, and if it can't be used as a swimming pool then it should be gutted and converted with additions....but not destroyed. Its part of Weston's seafront look and the exterior should be preserved for future generations and tourists to see.
Why do we to hanker to the past. Knock it down and build something stylish. I don't think the exterior is anything to write home about, you don't see hundreds of people swamping to the seafront just to see the Tropicana.
I've lived in Weston for most of my life and remember going to the pool before it even became the Tropicana. It's an eyesore, it's removed from the town centre and does not fit in with the new seafront. Knock it down, and I'm sorry to say the sea Aquarium as well, can't believe that ever got built. While I'm on the subject, I also have fond memories of the Old Pier. I grew up around that area and played on their as I grew up. But I think that needs to be knocked down and a complete rethink as well.
So in answer to the question, yes I do think they are right. Use the existing foot print and build a new modern purpose built indoor multi use arena for performing arts, music and special events with, I dare say a retractable roof for those occasional glorious sunny days.