I would love to ask our boss the following question.

HA, How many individual IT systems do we have, that if they fail, the whole operation stops?

I would bet he doesn't know the answer. I also bet it is a huge number.

For reference, I took a voluntary furlough and flew the bus for a couple of asian carriers. Both used the most basic "flight department in a box" that Airbus supplies. Paper manuals, PC based flight planning for dispatchers. Airbus will sell you a high tech version, but both carriers I worked for used the most basic. I believe Boeing offers similar products.
As far as I know, there was not a single IT system that if it failed, the whole airline would shut down.

We, and other legacy carriers, never had a plan to become the cluster#@$% of ancient IT systems that we are. It just happened. Going forward, we (and other legacy carriers) need to massively simplify and modernize.

Unfortunately it doesn't appear that our Flight OPS leadership even have a plan. Our IT department probably are not airline people, and don't understand what we need.

How many IT systems do we have, that if they fail, the whole airline shuts down?

In a perfect world, the answer would be zero. The second best answer is "as few as possible".