I am saying a light jog (LSS Run) will actually achieve the aerobic benefits much better. The Kettlebell work will get you better at doing a specific amount of reps with an exercise for each interval or for a specific time period. After the initial adaption, you will just get better at swinging the kettlebell for example. Strongfirst does have a full system though.
My issue with these programs is they claim to do everything, but it kinda just does everything to a lesser standard. Kettlebell axe will build you aerobic system if it's already poor, it will make you stronger if you are weak and it will make your strength endurance better if it's already poor. After that initial jump it's just you getting better at doing your chosen protocol.
I am a big proponent of MAF(maffetone) style running for building aerobic capacity. They even recommend it in the program and reference trying to use swings to achieve this, why not just run 1-2x a week, do some power work and some strength work? It's a good short term generalist program, but you would get more from building the ability to run for 30-60 mins 2-3x a week, provided injuries aren't an issue for you.
Plus you get the added ability of developing an extra skill like running, as opposed to getting good at standing in one spot swinging a kettlebell.