Using "can" to express future ability

I think the difference has to to with the particular meaning of the typewriter sentence.

In the latter example, the sports match, you are talking about a hypothetical, something that can, but will not necessarily occur. Can suggests the possible, but is mute about the probable. The phrase will be able also may be used to convey that theoretical possibility.

In the first sentence, you are not talking about a theoretical state of affairs, but a predicted achievement that you fully expect to realize.

I will be able to use a typewriter perfectly after a few more lessons, just you wait and see!

The word perfectly and a few more lessons makes this a very specific predicted outcome, rather than just a possibility.

If you were talking about a more general condition, say, under what circumstances can a person learn to use a typewriter perfectly, you could say

You can learn to use a typewriter perfectly after only a few lessons.

This is again theoretical, not predictive of a particular outcome.

The first sentence (I'll be able to use a typewriter perfectly after a few more lessons) is clearly about an ability that does not exist now but will exist in the future. This is why it has to be will be able to; can does not work in such a context.

In the second sentence (We can sit at home tomorrow ... ) can is more about a present possibility than a future ability. That is why the present tense can be used.

Here are some more sentences exemplifying the difference:

Our baby will soon be able to walk.

I don't think I'll ever be able to play the piano.

..

The doctor can see you first thing tomorrow morning.

I can provide the sound system for your party on Friday.

Comparing your answer with what I read in my grammar book and what I know as an almost fluent English speaker is that "can" in the future can't ever be used as an "ability". If I'm wrong, could someone give me a clear example of it?