I think those are reasonable considerations in such a system. However I also believe that weapon systems all have strengths and weaknesses that are combined with other weapon systems to create a complete war fighting capability.

When you consider fueling options, its true that solid rocket fuel is a much better choice for a weapon system that is not re-usable. But when the possibility of re-use is there, the calculus changes. The US ICBM system is a "last resort" type system and as such doesn't have a good re-arming (or re-fueling) capability. But the reasons for that are that lobbing tens of megatons of nuclear fire over the horizon really means that there isn't going to be much left of civilization when you are done. When you consider the submarine fleet or the bomber fleet (the other two points of the nuclear trident) there is a lot of infrastructure and cost associated with refueling capability for the delivery platform which are planes and subs. Until SpaceX (and perhaps soon Blue Origin), there hasn't been a "reusable rocket" delivery platform and so refueling capability has never added value over non-refuelable solid systems.

Further, intercontinental missiles are not generally considered a conventional delivery mechanism because of their expense relative to their payload. They only made "sense" economically delivering nuclear weapons since the cost of a nuke was high, but its impact was also quite high, and so as a means of projecting force on a global scale it had high utility. But that changes too if your
"marginal cost" is the payload and fuel. It is a well understood process for creating LOX and LH2 on site, Kennedy space center already has that capability.

Your second point, about turn around time, is also a good thing to consider for any weapon system. For conflicts against enemies that don't possess and intercontinental capability, cycle time for firing from the Dakotas in the US can be quite long as it would require a conventional army to traverse a large portion of the US or Canada before it could get to the base. That is very expensive and hard to do. Thus even if it took a month between firings you would not be in any danger of being destroyed. But systems design also tells us that we can finesses long cycle times with parallelism, so a network of 30 bases could fire one chunk of payload once a day (once from each base) continuously. That is just a question of money.

But all of this sort of speculation simply reiterates the point around peaceful capabilities (resuable rocket boosters) which have very real strategic implications. And space (and NASA) are particularly compromised by this. The US rocketry program was lead by Werner Van Braun after all, who had been using his developing knowledge of rockets to bomb London from Germany. The entire early space program was simply a palatable cover activity for developing reliable ICBMs with systems so integrated that nearly all of the satellites the US flew into orbit used an ICBM rocket body to launch them. This history has influenced NASA policy since its inception, delicately walking the line between "It's Science!" and "It's Military Superiority" in the capabilities they researched and deployed. As private companies develop more of these capabilities they won't stop because "it could be dangerous" and the military will have the same problems it did when the semiconductor chip industry ran ahead faster than the military could. You have to reach a new place of understanding where "commercial tech" >> "military tech" for some definition of 'tech'.