Should the UEFA Europa League winner or the UEFA Super Cup winner qualify automatically for the next Champions League?

No. But don't jump the gun too fast here. Here are my 2 cents : Based on the question description, I think your concern here stems from the fact that Europa League has been positioned by UEFA as an unappreciated sibling of the CL in recent years( A point with which I concur). I believe that league standings are a fair criteria for admission into the European competitions because they underline the consistency of the teams. Instead of using Europa League/Super Cup competitions as a qualification route ( Incidentally, I am also against 3rd placed teams in the group qualifying for Europa League as this just builds upon the notion that Europa League is undervalued), I believe that UEFA should build a lucrative brand for Europa League. This will encourage competition for the top-half of the table and will hopefully enable mid table teams to gradually transition into European powerhouses. And maybe, just maybe, we won't have coaches/players  crying over fixture congestion due to participation in the Europa League again.

No. Merely because it would undermine the Europa League in itself and label it just as a stepping stone to greener pastures.

I asked the question, and I think I should write an answer to explain why I think it should be so, to gather my arguments in one place: In the first place, the Europa League is considered beneath the Champions League by every one. It's status is always below that of the CL. Ask the fan of any team winning the EL if they'd have their team in the CL instead of the EL next season, and what do you think they'd answer? Yes, of course. This subservient status is reinforced by teams being relegated from the CL to the EL and teams like Manchester United and Manchester City not even bothering to compete. As for the status of the teams winning the EL, for the last ten years and more, the EL winners have been teams that have also played in the CL once or more in that same period: Atéltico Madrid, Porto, Sevilla, Shakhtar Donetsk, Zenit St Petersburg, CSKA Moscow, Valencia, Feyenoord, Liverpool... That these teams have also managed to get in the CL during that period says something. Also, what about the teams that won the CL without winning their league the previous season? They are hardly "champions", to play in the "Champions" League. In England, there are playoffs for the 3-6 placed teams in the Championship to decide who gets into the PL. So we have some  precedent of promoting teams to next level based on games in addition to  their league standings. The Champions League play-offs usually involving teams that just barely qualified to the CL. Surely an Europa League winner is at least on par with these teams? Atlético Madrid played 19 EL games last season. 19. That's half as many as their league games. Porto played 17, I think. No Champions League winner plays as many (typically about 13 games - 25% less). That's hard on any squad. To play that many games and still improve their league position is beyond all teams in Europe, except perhaps for the top ten teams in the leagues combined - teams like Barcelona, Real Madrid, Bayern Munich and Manchester United. For all this, the prize money that the EL winner gets (excluding TV pool, if any) is less than 60% the prize for getting into the group stage of the CL. Think of it. An EL winner gets into the playoffs, wins it and their prize money and thus their spending power for that transfer window is more than doubled. An EL team has to suffer many of the same problems as their CL counterparts: long flights, extra midweek games, increased fatigue - all for less than what a team that doesn't even clear the CL group stage gets. Atlético Madrid won the EL. But their financial stability rests on getting into the CL. They wouldn't care about winning the EL if that stood in the way of getting into the CL. And I think that showed this year for a club that has won the EL twice in the past three years. Think of fans of a club winning the EL: Will they say "Boo! We won the EL and now we have to be in CL next year!" Ridiculous. "Yay! We won the EL and now we get to be in the CL!" is more likely. Guess what they'll think if they won the EL and qualified to the CL via league: "Yay! We won the EL and now we get to be in the CL!" Finally: Wigan has won the FA Cup and been relegated. Thus, a Championship team will play in next year's Europa League. Consider the highly improbable - who am I kidding - impossible situation where they win the EL, thus qualifying for the CL and then doing some giant-killings there, maybe even win the CL? Tales from which legends are born.