Why hasn't warm dark matter replaced cold dark matter as the standard model of cosmology?
I stumbled on this question and thought I will give it a try, hopefully it is still relevant to you. The thing with all the issues you cite is that they have a solution within $\Lambda$CDM
Too Big to Fail problem I think this problem is overrated. Within a couple of weeks of its publication people already found solutions, even with more colorful names: Vera-Ciro et al. (2012), Wang et al. (2012), Brooks et al. (2012) ... and the list continues. Point is that it is not an unsolvable problem within the list of things we know. For example, the first two references argue that the number of massive satellites strongly depends on the mass of the MW, which is actually a pretty tough number of measure, so moving the virial mass of the MW to the lower end of the spectrum is perfectly valid.
Baryonic solutions to the problem are also available, based mostly on feedback. But here is the deal: if you throw away CDM in favor of WDM, these two things (MW mass and feedback) are still going to be there, the result is that you're going to overshoot the problem in the other direction. Now you will end up with the opposite problem. I will call this argument (A1).
Cusp-Core problem Again, we know solutions for this problem within $\Lambda$CDM, a couple of SN can cause a lot of damage. Even with a modest stellar formation history in a gas-poor dwarf you can expect to have a modification in the inner slope of the host dark halo, e.g. Breddels et al. 2015. I've never tested this myself, but I have the feeling that if you run a simulation with enough resolution to resolve small structures in WDM and add feedback in a self consistent way you will end-up with no cusps at all. Again (A1) applies.
Unfortunately, I don't think WHM is popular enough to try this type of simulations with the level of details of say Illustris
Missing satellite problem I don't think this is a problem at all. It just reflects the free market nature of physics: big things end up bigger, small things ... well. You can come up with a convoluted story to about the way dark matter could affect this problem, but at the end a simpler solution will work better: cooling in small halos is insanely inefficient.
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I will stop here, but I think you can see the pattern. Cooling is a real issue, baryonic feedback is real, mass uncertainties are real. If you solve all the issues you post with replacing CDM with WDM all these processes will still be there, affecting how galaxies form, and the solution that WDM offers will not longer be valid.