If it ever becomes a world reserve currency used for payments all around the world like some people believe we will have to think of something.
By the time Bitcoin reaches 21 million we will probably have at least 1/4 of that permanently lost and another 1/4 in safe accounts of lifetime hodlers which will leave only 10 million in circulation. That's not enough for over 500 million people. I said 500 because not all people in the world will use Bitcoin just like USD and EUR are estimated to be used by about 350 million people each.
Yes and no. I don't think that we will ever need an increase in the max supply, and you have given the reason right there, even if we get very widespread adoption, it'll prolly never go over 500m users, and 10m btc is more than enough, if it isn't, then price will increase and it will fit, as long as the chain can handle the traffic we should be good, there'll be a point where we'll switch from large transactions (0.01 or more btc) and, let's call it regular transaction volumes. To a smaller transactions (sub 0.01) but in much greater volumes, and it'll be dictated once price rises.