Well, the million-dollar question, so here are my two cents. First, it would be much easier if I could tell you because of money. In this case, we would be done right now. Everybody would understand it. Our primary motivation as a person is money. Which is understandable because of the world we live in.
On the other hand, this question stinks. It is a shame that many great experts - myself not included, I am not an a11y (accessibility) expert - must answer it. It is a shame that we have to argue for a11y.
For the first time, we can create a genuinely inclusive thing, media, etc. So why not? Why not make something (or many things) that serves everyone equally?
In this life, tremendous things are exclusive, which we can't make much about. But we can make slight differences. And I know it doesn't mean much, but it is something. As web designers and developers, we can create inclusive media that help people, not mess with them.
Adding a good quality alt description and correctly using the button element is small but can help a lot in the long run.
- Caring about accessibility is the right thing to do. It can be a business decision or a law, but mainly it is social responsibility. You also do this for yourself, your future self, because you will be old (hopefully) when your cognitive capability, mobility, vision, and hearing start to decline.
- The world needs someone who cares just a little bit more. Who gives a shit. Anybody can be that person on a low budget.
- If you are a government entity, there is no appeal. Besides the related laws, you serve the people, all of them. Your goal is to be inclusive. So this article, opinion is not about you. If you aren't inclusive or not trying to be more inclusive, you have failed your people.
- Well, this is still capitalism, so care about accessibility because it makes a lot of money. Of course, it depends on the context.
- A11y is UX; usually, when you make something accessible, you do not just help the people that need it the most but all of them. The low-floored buses and trains are a good physical example. It is a must if you use a wheelchair or push a baby carriage. It will help the elderly, persons with temporary injuries, and everybody because it is easier to use.
And when you create inclusivity in mind, you will make mistakes. Everybody does, don't overthink it. Start small and be consistent. The main thing here is that you should start to care about accessibility.
Check out Bite-Sized Accessibility, where you can find short posts about a11y to help you start small.