the following is my analyses, not my opinion on what should happen
Much of the response of the Non-charedi segments of the population to the BaGatz decision is rose-glasses at best, ignorant at worst.
Most of the Charedi world will do the same thing to the draft notices, that the Yishuv Hayashan (Eida Chareidis, Stamar, Etz...) have been doing for years. Ignore them all.
The only reason that they were showing up in the first place to the draft boards was that at the end of the day, they got a deferment, and eventually an exemption. It was pragmatism, not recognition.
Now that that doesn't exist, there's no reason to pay any attention. (This doesn't mean that the kanoim were right the entire time, rather circumstances change)
In some ways, it will do good things in ruchnius for the society.
That's the end of bachurim and young avreichim taking vacations in Chul. (Can't leave the country if you are a deserter).
There is no longer a need for imaginary yeshivos for weaker talmidim, just to get an exemption while they are otherwise leading productive working lives. (True, there were those that this maintained the connection, but for others it is better to move on and call one self a koveh itim, rather than a ben yeshiva).
In other ways it will be bad.
True, there will be a percentage of those who were on the fence (weaker sfaradim, some of the so-called Charedi Hachadash, certain more anglo olim...) who will now do some sort of national service, whether in the army or sherut leumi, but nowhere near the 25% that the army is predicting will comply with draft notices.
It is truly unknown what the short to medium term macro economic ramifications of ending the current financial arrangements will be.
Will there be a major uptick in chareidi defaults on mortgages? what will that do to the wider banking system?
Will more people (men) enter or (women) leave the workforce due to ending the daycare subsidies?
How will the chareidi focused business react to less fluidity in the financial pool?