You can certainly dive with tables, for sure, but they are much more conservative than computers, as they are based on a square profile (deepest depth is the only depth) & as most recreational dives are multi- level. A computer is constantly recalcualting your bottom time based on your current depth & dive time. Yes, this can also be calculated on the wheel,... but do you really want to keep interrupting your dive to recalculate your nitrogen loading? My favorite personal example of the value of a dive computer, is a dive I did in a blue hole. I went to 130 ft, which by tables, has a maximum bottom time of 5 min. (not even considering the residule Nitrogen form previous dives). By going to depth for just a few minutes, then working my way up the wall of the blue hole to a reef on the edge at 40 ft, I was able to stretch that dive into a 45 min dive & was no where near NDL's when I surfaced. If I had used regular tables, I would have only had a 5 min. dive plus ascent. I like to do longer dives. That said, I do persoanlly teach my students both tables & computer diving, so that they understand each.
When all is said & done, basic dive computers aren't all that expensive ($200 or so) or hard to use & they give you much more bottom time.
As for your last question, yes, computers are slowly becoming the mainstay of diving, but there will always be those who will use tables, no matter what....