Leave it alone if
- The site is fine. Nobody reports it as slow, no resource notices arrive, the usage graph is nowhere near its ceiling. A site that is comfortable on shared hosting can stay there for years.
- Somebody quoted it without measuring anything. Ask which resource ran out and in which window. Anyone who cannot answer has not diagnosed anything, and "future-proofing" is not a measurement.
- The slowness is an image problem. The common case by a wide margin. A photo straight off a phone is many times larger than a web page needs, and a page carrying a dozen of them is slow on any hardware you care to rent.
- The site is on a platform. Squarespace, Wix and Shopify include their own hosting. A separate plan would sit empty.
- You are rebuilding soon. Put the new site where it is going to live and skip the move in between.