Republicans have chosen this (at least some of them) because the political ramifications of choosing to "let Obama care implode" are potentially even more severe than simply trying to repeal and replace it.
Even if the arithmetic implies that allowing an implosion is (dispassionately) the "right" way to let things happen, the GOP might actually possess a modicum of empathy for the victims of 0bamcare.
Entitlements, in general, can be dealt with, and they will be, eventually. But it's likely to be done less with strident rhetoric, and more with policies which help create jobs and encouraging social mores which stigmatize dependence on government. Certainly starting with such measures isn't the best choice.
Much better for the President to get his feet wet by saving some of the most sacred cows for a later date.
Then, as the entitlement state naturally shrinks for reasons of good government policy and increasing national prosperity, it will become at least somewhat less controversial to dismantle it, or at least reduce its scope and application.
Let's not forget that immigrants, both illegal and otherwise, are disproportionately represented on America's welfare rolls. First things first.
If Senators like Ted Cruz and Representatives like Rand Paul win the day, we will get real reform and improvement, not just the window dressing that the appeasers want. I believe the President is more in line with the thinking of Cruz and Paul than the squishy "moderates"...
The reality is that entitlements will not be dealt with in the ordinary course of politics rather they will be dealt with in the ruins of a broken economy. They have not been dealt with since Franklin Roosevelt and there is simply no prospect they are going to be dealt with now except that Trump, under the influence of Ivanka, promises a new entitlement and has even assured the public that he will not touch any entrenched old entitlements. He has made promises about Obama care that simply are arithmetically impossible and it is time even the most rabid Trump supporters acknowledge that.
That is why many of us advocate for Article V movement that, if accomplished, would actually restructure Washington so that the entitlements vortex can be ended. But but I do not believe that Article V will be accomplished unless and until there is a crisis of some sort. A reckoning if you will. That is what I meant when I said that you are correct, entitlements will be "dealt with" but only when we have no other choice.