Foam or No Foam? 1973 14' Terry Bass Restoration

OK, I'm new to this forum and new to boat repairs.
I am mechanically inclined (in the process of doing a shell off restoration on a 1974 27' Airstream.)
The current project is a 1973 14' Terry Bass boat restoration.
Engine (original 1973 Johnson 40 HP Seahorse) has been completely overhauled by Stone & Sons Marine in Houston and it performs flawlessly.
My goal is to restore it to "almost new" condition.
The exterior of the hull is in good condition and the transom is solid. It's was never drilled for the engine to be mounted.
The floor was spongy so I decided to pull it up as the previous owner had done a hack job repair.
When the plywood was removed and the closed cell foam exposed, it was holding water.
My question is: Is it really necessary to replace the foam after its removed? I plan to replace all rotten stringers and overlay with 3/4" marine plywood.
I've seen some information that suggest that the foam will alway hold water and add weight.
Any insight would be very much appreciated.

kimcrwbr1,
Thanks for the information.
I am just getting started and not far enough along to know if there's room for an "in-hull" fuel tank, but that sounds like a great idea.

kimcrwbr1,
Yea this is fun (NOT)!
The stringers are defiantly coming out and new ones going in.
My plan is to restore to original design with stick steering. The current stick steering and cable steering is not 100% original. Previous owner did a crappy fix and I'm not satisfied with it. I will probably use a new "Ezy-glide" system. Looks like they're the only company that manufactures a reliable stick steering system.
If you read my previous thread I explained my reasoning for taking on this project.
Nostalgia has it's price.
I've never worked with fiberglass, but looks pretty straight forward.
Thanks for the advice and please keep it coming.

BTW, here are some photos. The one with the truck is the day I picked her up. Craigslist purchase for $1100.
Next photo is after some elbow grease on the finish.

Foam out! Finally

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I would be very careful pouring foam with the deck laid on an already, I have seen some boats with the floor buckled from the foam.

Every small boat I have owned, I used expanding foam in the floor. It supports weight, quiets the boat, and the foam I use doesn't take in water. I usually tilt one end up and pour about 1/3 of the needed foam. Then tilt the other end up and do another 1/3. Level the boat and finish with small pours. I usually use a hole saw to make about a 2-3" hole and save the cut out portion. Once the pouring is done I remove foam in the hole until the cut out circle lays flat and pour epoxy to fill the cut and center hole. Then epoxy resin 2.0 rsm over the deck. I know that lasts 30 years with care.