The fact that healthcare providers could use external staff such as IDF medics only strengthen my point. Even though is just a drop in the ocean of the vaccine task force.
I haven't seen any other resource says IDF transporting the vaccines. Teva is the responsible of that and it's not an issue. Neither about anyone who is not soldier and got vaccine at IDF.
The Covid tests in Israel are nothing to be proud of.
IDF isn't involved in the vaccine rollout.
And if your point was right, the lockdowns in Israel would have been much more effective and on time.
The reality is the the first lockdown was removed too early, and the other lockdowns started too late with lame enforcement. Everyone who watches news in Israel can tell you that.
Israel has competition between several private healthcare providers. That fact makes them agile and efficient than most places in the world (e.g. Britain's NHS ).
The army has nothing to do with the vaccine rollout.