No, and discard this contractor who recommended that nonsense!....

IMO

It depends on how long you plan to live in this home.

A heat pump system is merely a air handler and out door heat pump condenser.

An air handler is a coil, a blower and series of electrical heat strips.

If you replace the heat pump condenser and indoor coil, you have an old blower, old heat strips and old relays to control everything.

Electric furnaces can be repaired by the 'skilled' contractor. The unskilled will tell you to replace everything.

In some cases you may have to replace everything as such if you are looking for higher efficiency system.

Additionally the newer coils may not fit the existing air handler. In situations like that you are better off replacing the air handler.

No matter what you decide to do: You will ALWAYS need a good HVAC Repair man.

I service the Katy, Texas area.

What is your location and what is the size of your house?

Can you post one of the extremely high quotes with the model numbers of the equipment? You may have been quoted an over sized high end system that is expensive and inappropriate for your climate and house. You should be able to find a good system that is reasonably price.

Depends what you mean by extremely high. Can you post the quotes (cost, equipment)?