This is a common question that generates a bit of heat (as you've seen with Zeta, and I'll chime in with later).
To answer the question in your title, yes, anyone with a valid WDW ticket may use the WDW transportation system to get around the resort complex. The price is included with the admission media.
To answer the question in the body of your post (as Tink already did), no, it is taboo to park at a WDW resort in an effort to avoid the parking fee. Likely, this is exactly why the resort in which you are staying has the transportation charge, as many people not staying there have taken advantage of their "free" shuttle. Otherwise, the price would be included in the room rates/member dues. In essence, you are feeling the pinch of this same thought process.
That said, you are going to enjoy having your own car versus using the WDW transportation as you suggested mainly due to the flexibility this option offers. At the end of the day, you are going to be tired, and a nice comfortable vehicle waiting for you in the lot is going to be much more appealing than waiting for a bus with hundreds of other guests staying at the resort in which you parked. It really is nice to get in the car and drive directly to your resort versus fighting the crowds.
Lastly, as a bit of a purist when it comes to first visits, I feel it is important for first-time visitors to drive to the MK! The excitement of driving under the arch, through the ticket booths, riding a tram to the Ticket & Transportation center (TTC), then hopping the monorail or ferry to the MK is the way entry was designed to be experienced. The trip is just as important as the destination at Disney, and the queues are designed to set the story before getting to the ride. Sit back and enjoy!
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Thank you for this reply.
I had actually missed all of the responses after the first. I guess I didn't click on the link in the email so it stopped notifying me there were replies.

Your comment about the comfort of having our own car there is exactly what I needed to hear. I've never been to WDW before. I was afraid having to drive our own car would be stressful or difficult (I've heard traffic can get bad). BUT we'll be there in the fall so I'm thinking that may be less the case anyhow.
Really $15/day (or thereabouts) sounds like it will be well worth it.
I am very big on "my time is money" and am definitely willing to pay a premium for convenience. It is fabulous to know that having a car there is an asset and not a liability.
I am also looking forward to the traditional entry to the park as you described. Thanks for painting that picture so well.
Thank you! And I'm sorry I started a thread that created some heat. I am learning as I go along.
