1) Orbit Insertion

You have to be able to slow down at the end of your journey. On a short trip (by astronomical standards) like the moon, you only have about a short time/distance to accelerate before you have to start slowing down so you don't blow right past your destination and instead of being able to hit the right speed that allows you to enter the orbit of the celestial body
 
The trip to the moon is very short (in astronomical terms) - only ~384,000 km. They didn't have any room (nor need) to speed the spacecraft up much faster than the 3,000 kph referenced. It's kind of like if you're just driving 5-6 houses down the street to the neighbor's , you'd never going to need get our of 2nd or 3rd gear or exceed 25 mph, because as soon as you got up to that speed, you'd already be having to start to slow down in order to stop at their driveway and not blow past it. So there was neither time nor space (pun intended) available to actually build speed beyond that 3,000km velocity.

You can also imagine this as analagous to taking you take very short flight of only a 50 miles or so (i.e SLC to Provo). The airliner will never reach anywhere close it's ~600mph cruising speed, nor it's cruising altitude of 30,000 ft at which it's capable of flying. It's still in the early part of it's climbing stage when it becomes time to start descending.

Mars is about 150 times farther away. So, like a car that has a few hundred miles to travel instead of a few hundred feet, the car has the time/room to get on the highway, and accelerate all the way to 80mph in top gear, and then stay traveling at that speed for a long time before it has to start slowing down near the destination.


So far, every single mission to mars (including fly-by probes those that slowed to deploy landing vehicles) has been undertaken in less than a calendar year (most less than 300 d
In the airliner example, this is SLC to ATL, where you have time to reach full cruising altitude and therefore cruising speed of 600mph at 30,000ft.


2) Fuel and Payload limitations

Apollo had to carry all the fuel it needed to not only accelerate the lander and craft, but also slow it down, and maneuver it. The faster you go, the more fuel you need to slow down on the other end, the more fuel you need to carry with you, the more fuel it takes to accelerate, and round and round. It's a circular problem that becomes exponentially more inefficient beyond a certain point. Apollo could carry a very minimal amount of fuel to use to slow down and maneuver into lunar orbit, so it couldn't afford to go much faster than the absolute minimum to escape earth orbit and reach the moon with minimal need to slow down.

Starship, on the other hand, will be able to refuel itself after launch, so it can "start" the journey to mars with a full tank of gas, and be able generate it's velocity in the vacuum of space.

Additionally, it is under less time pressure than Apollo was to get going right away due to limited/primitive life support systems and power/food reserves.

Starship can afford to take more time in orbit to take advantage of gravity assists of both Earth and potentially the moon to get moving faster as in a more fuel efficient manner.


3) Other misc reasons, such as higher launch velocities and other technological improvements. Starship will be able to be moving faster than the apollo missions were when they hit LEO to begin with, and they have much more efficient vacuum engine as well to be better able to accelerate.


Of course this isn't comprehensive, but you get the gist that the moon was a chip shot, and Mars is a driver off the tee box. Chip shots are soft touches that aren't hit nearly as hard, nor with as big a club as a drive. Accordingly, the club head speed and ball speed are much slower and not useful comparisons for extrapolation of travel times.


So far, every single mission to mars (including fly-by probes and vehicles that slowed down to orbit and deployed landers) has done the trip in less than a calendar year (approx 7-10 months). Technologically, speaking, even a scaled up Starship trip should be doable in 9 months or so, potentially faster if refueling becomes possible on the destination planet so you can afford to burn up all you fuel on the way there.

Even if it did take twice that, say 18 months, the technology exists to run life support systems for that length of time, and humans have already demonstrated an ability to operate for a year in space, so a 1-way trip is feasible even with that travel time.

Frankly, the real issue with humans on Mars is the prolonged exposure to zero gravity, and then ~.4 gravity for the years that would be required to make a round trip mission. You'd come back to Earth and be unable to walk and potentially with severely deteriorated bone density, organ weakness, etc that might take years to recover, if at all.

But, I digress.

And I fully understand I've wasted a bunch of time with a serious response to what is like not a serious comment.