The large rocket adddresses basically all the problems.
Time between resupply? Well, you can just take a bunch of resupply missions with you. Most stuff is packed ahead of time, except fresh veggies and fruits, but deep freezers can keep the nutritional value of those nearly as well as being fresh.
Redundancy/reliability? Bring the spare pool with you instead of keeping it on the surface for resupply flights. Bring two different systems.
Long duration life support? Enough mass allows you to avoid it all together if you like. This still has not sunk in to most of the fairly educated people who opine on this topic. Simple life support systems are VERY reliable, and the advantage of advanced life support systems is they reduce mass. If you don’t need the mass reduction, you don’t need the advanced life support.
Far from medical care? Small crew sizes are a mass constraint. More mass means you can afford large crews with dedicated medical personnel. And the equipment to go allow with it.
Also applies to radiation shielding (mass) and even partial gravity (centrifugal gravity is well known as a replacement but for some inexplicable reason is avoided… and yea, even short arm centrifuge is useful and could be used on the surface… the disorienting effects are actually manageable, and while in space, a tether can be used to enable long arm centrifugal gravity with little Coriolis effect).
Transit times can also be reduced significantly with refueling. 80-120 day transits are feasible, not just the most efficient 150-210 day transits for long stay. The surface of Mars also has significant radiation shielding in spite of the thin atmosphere. The Mars rover Curiosity measures the same radiation equivalent on Mars’s surface as on ISS today. Mars rover Perseverance also demonstrated production of unlimited oxygen from the Martian CO2 atmosphere using electricity. Regolith could also be used to enhance radiation shielding. This is before discussing water mining (and even that can be done without touching regolith, just the air using the WAVAR technique… useful for crew consumption although this method doesn’t scale up to producing enough for propellant very well).
There is no a single hazard or obstacle to a Mars mission that isn’t at least partially mitigated by having a lot more mass capability, ie a big and cheap reusable rocket (capable of landing on Mars and aerobraking).
Well there is the "one-way trip" version which takes out some risk but trades the risk of losing 4 astronauts for the risk of losing 400 or more.
Since it's not plausible that you could bring anything back from Mars that would be worth enough to make colonization practical from the perspective of Earth, Mars colonists would always have to assume that the last rocket that was launched is the last that will arrive. From their point of view, they'd want to be able to manufacture absolutely everything locally as soon as possible.
It's one thing to say "we can make unlimited oxygen from the soil never mind the atmosphere", it's another to find a source of nitrogen or other inert gas that makes it possible to live in an atmosphere that doesn't make everything into a firetrap. It's one thing to spin the kind of science fiction that Gerard K. O'Neill did, but his disciple Eric Drexler realized just how bad the problem of 'advanced manufacturing' is and went off to follow his own El Dorado, writing a fascinating book [1] about a class of systems that 'just don't work' [2]
Not to say that the goal of "a population of 10,000 people being able to make everything that 8,000,000,000 can make" is unattainable, even if we can get it down to an advanced industrial base being supported by 10,000,000 people it would be a game-changer here on Earth. I can see paths there, but it's by no means a bird in the hand.
It would probably be smarter to launch multiple payloads than have everything in one big payload, a fire can take out the primary and redundant supplies for example.
That said, throwing more money and gear against the problem will likely be the way to go. Besides, it doesn't actually have to be done all in one go, if the vision of SpaceX is that of mass production, they can launch a whole chain of Spaceship sized payloads towards Mars years before a human crew is sent that way, giving them supplies and whatnot on the way, in orbit, and on the surface. That'll require a lot of planning and automation though.
This is irrelevant and completely ignores the OP. We've had rockets capable of going to Mars since the 60s. More rockets do not solve the problem. Cheaper rockets do not solve the problem. Please read the article.
Time between resupply? Well, you can just take a bunch of resupply missions with you. Most stuff is packed ahead of time, except fresh veggies and fruits, but deep freezers can keep the nutritional value of those nearly as well as being fresh.
Redundancy/reliability? Bring the spare pool with you instead of keeping it on the surface for resupply flights. Bring two different systems.
Long duration life support? Enough mass allows you to avoid it all together if you like. This still has not sunk in to most of the fairly educated people who opine on this topic. Simple life support systems are VERY reliable, and the advantage of advanced life support systems is they reduce mass. If you don’t need the mass reduction, you don’t need the advanced life support.
Far from medical care? Small crew sizes are a mass constraint. More mass means you can afford large crews with dedicated medical personnel. And the equipment to go allow with it.
Also applies to radiation shielding (mass) and even partial gravity (centrifugal gravity is well known as a replacement but for some inexplicable reason is avoided… and yea, even short arm centrifuge is useful and could be used on the surface… the disorienting effects are actually manageable, and while in space, a tether can be used to enable long arm centrifugal gravity with little Coriolis effect).
Transit times can also be reduced significantly with refueling. 80-120 day transits are feasible, not just the most efficient 150-210 day transits for long stay. The surface of Mars also has significant radiation shielding in spite of the thin atmosphere. The Mars rover Curiosity measures the same radiation equivalent on Mars’s surface as on ISS today. Mars rover Perseverance also demonstrated production of unlimited oxygen from the Martian CO2 atmosphere using electricity. Regolith could also be used to enhance radiation shielding. This is before discussing water mining (and even that can be done without touching regolith, just the air using the WAVAR technique… useful for crew consumption although this method doesn’t scale up to producing enough for propellant very well).
There is no a single hazard or obstacle to a Mars mission that isn’t at least partially mitigated by having a lot more mass capability, ie a big and cheap reusable rocket (capable of landing on Mars and aerobraking).