I much prefer multiple alternatives as then SpaceX can't do price hikes. For example, the US has paid russia to send rockets to space since before they cancelled the Space shuttle. But once they did, the prices went up drastically.
The more competing options there are, the better.
This. Competition.
For lunar operations you might need to put fuel tanks inside the trunk & the make the fuel usable to the thrusters in the capsule.
Or alternatively put some simple thrusters in/on the trunk. These could have more efficient nozzle compared to what Dracos & Super Dracos have due to capsule aerodynamics constraints (compare the nozzle bell size for Orion and Apollo). On the other hand this would increase complexity quite a bit & you are effectively lugging around duplicate engines.
As an avid Kerbal Space Program player (but not a rocket engineer!), I feel like it shouldn't take that much effort compared to what SpaceX has already done. Given that Falcon Heavy has the capability to get the Lunar Gateway to Lunar orbit (1), one Falcon Heavy should easily be able to get a robotic tug in LEO and another FH launch could get one in orbit around the moon. Then the Crew Dragon could launch on the Falcon 9, rendezvous with the tug in LEO and then go to the moon. To land I expect a special trunk with it's own Super Draco engines and fuel could land the capsule on the moon and take it back to orbit, potentially with help from the capsule Super Dracos as a sort of second stage. The Dragon would then rendezvous with the second tug that takes the capsule back to LEO so that the reentry would be at already certified speeds. This way nothing would have to change for the Crew Dragon itself so it wouldn't have to be recertified.
With this plan the only new things SpaceX would have to make would be the robotic tugs using vacuum optimized Merlin engines and a special trunk for the Crew Dragon that would let it land and take off of the moon. I do wonder if the Crew Dragon's life support systems are rated to last this long and out of LEO. It also would be a one shot program like Apollo which seems antithetical to how SpaceX operates, so unless Elon does it for bragging rights as the first purely private moon landing I don't see it happening.
(1) https://arstechnica.com/science/2020/05/nasa-planning-to-lau...
Basing this purely on my Kerbal intuition, SpaceX might try something along the lines of: 1- use a falcon heavy to get a tug (Merlin Vacuum rocket, plus big fuel tank plus docking port) into low earth orbit. Very soon afterwards, launch the Dragon to a rendezvous orbit with the tug. Meet, join, head out.
Dragon can land itself with Draco thrusters it already has and likely take off as well- if it has enough fuel. The Dragon might need to be modified for extra fuel.
Then of course it either needs a thicker heat shield or else more fuel to slow down before they hit atmosphere, whichever is lighter/cheaper to develop.
Could be done, but the R&D money for that could instead be put into Starship. Same story as the recovery of falcon second stage.
I have to disagree. For all the technological achievements of SpaceX, we still don't have the capabilities lost with the Shuttle. No other spacecraft before or since has had the ability to launch 8 astronauts and return multi-ton cargos from LEO. There was also just something so cool about having a freaking spaceship that capsule designs will never have, and that shouldn't be discounted. I couldn't help but feel somewhat depressed watching the Dragon launch like we have regressed as a society, no longer daring to push the limits and strive for absurdley ambitious things like the Shuttle did.
Dream Chaser too is dangerous since in the event of an explosion it will likely tear the wings off, making a safe return infeasible.
A slightly improved heat-shield and some rad-hard electronics would do it IMHO. That would save NASA another $10 billion or so.
I find the statement that there's a public desire for a winged spaceship silly. I haven't heard anyone call out for such a vehicle, certainly no chant from the general public. The dream of an airliner-like space shuttle died when Columbia disintegrated upon reentry.