I wish you're right, but I do think it's going to take more than an Arab Spring type of event. I picked Nigeria as an example because it's such a big economy, yet almost all of the wealth is in the hands of a tiny minority. The country is divided according to religious lines, and there are deeply entrenched local interests, so if there's an uprising it's likely some "old hands" from the current regime will maneuver and place themselves in a more advantageous position, and true reform will not happen. Also it's a huge country population-wise, so to implement any meaningful change the inertia will be immense.
(Quick aside: I am realizing I am implicitly using China as a reference for economical improvement, but not India as also mentioned by GP post, simply because some segments of the population in India still live in a horrendous level of poverty, and I think true improvement necessarily implies the elimination of extreme poverty.)
To keep the Arab Spring as a point of comparison: it did succeed in Tunisia because the population (1) is educated and connected, and (2) had an homogeneous view of where it wanted to go (politically speaking). This meant that even if not all "pro-regime" forces were cleaned out they still had to take a back seat in the new regime (example: their police forces), and alternative political movements such as the islamists literally abandoned islamism after a few years. In contrast in Egypt it failed IMO because (1) 25 % of the population is illiterate, so is not educated/connected/informed all that much, (2) had differing views, with a major islamist movement in place (that historically had basically grandfather islamist terrorism), and (3) some major "pro-regime" forces (in this case the military) were not reformed/removed and still had all the resources and levers they needed to depose the new government whenever they felt like it. So in the end Egypt returned to military dictature as quickly as it had left it.
Again, I would really be happy to be wrong, but right now if a revolution happens, Nigeria is more on the "Egypt" end of the balance than on the "Tunisia" one. If we look at all the revolutions or major reforms that have happened since the 1980s, the successful ones have always happened where civil society was past some education threshold and had a good cohesion regarding its ideological worldview (basically nation-wide support for secular democracy and the rule of law). That was the case from South Korea to Taiwan to South America, so I don't see why it wouldn't apply to Nigeria as well. Note that I'm NOT saying that there are no people educated/informed enough, what I am saying is that because your country is so big and the disparity so large, there are A LOT of people who right now are not informed enough and way too removed from any political discourse to be enrolled in a cohesive reformist movement.
That being said my point was specifically for the short time-frame being discussed (within 20 years). I don't think such a huge country can navigate through such deep changes that quickly, but it's very possible that much of the preliminary work (such as getting the majority of the population on the same political page) can be accomplished by then. For example it's possible that because your educated youth is fed up, an anti-corruption advocate or national-level politician will gain significant prominence and start pushing the country in the right direction.