Ok, here is my rationale: 1) neither competition is particularly valuable in any country (bar maybe the supercup in Spain), 2) these both lead to fixture congestion (especially the league cups), and 3) there are far better ways to blood youngsters than league cups (which tend to have awful attendance figures in almost every country the exist). So, should they be scrapped?
What do you mean when you say "league cups"? It's not very clear. But regarding the super cups, I say you might as well keep them. It doesn't add to fixture congestion since they're mostly played in preseason. Yes, they're pretty meaningless but so are ordinary preseason games. So if you're not playing a pre-season super cup game, you would just be playing some other preseason game (maybe even in a different country or continent), thus they don't add any games to a team's calendar.
League cups are a country's "second cup." Whereas primary cups (FA Cup, Coupe de France, Coppa Italia, etc.) include a large number of clubs (both professional and amateur), league cups (which are only played in 14 of 54 European countries) include a smaller number of clubs (usually only professional clubs), are less prominent than the primary cup, are used to try out youngsters, and, unlike primary cups, usually do not offer the winner a place in the Europa League. A.k.a. they're pointless.
League Cups - yes, for all the reasons you said. Big clubs tend to use fringe players has they are sandwiched between European dates and they see very little point in sending star names out against lower tiered opposition. The major league cups (well, certainly in England) started well before the expansion of European competitions so there was space in the calendar for the competition. Today, we have youth/reserve leagues, reverse teams playing in the pyramid (not in England, though they have been pushing for it) and the UEFA Youth League - there is plenty of opportunity for young players to play. I am sure reserve players for Chelsea/Man City/etc would rather play other reserve players than the full squad of Accrington Stanley or Crewe Alexandra. As for Super Cups - I had the same opinion as League Cups, but I am starting to come around that they arent exactly useless. They are in preseason, so doesnt really lead the fixtures issues and it is a nice way to start the domestic season.
https://en.wikipedia.org/wiki/2016–17_UEFA_Europa_League#Third_qualifying_round has spots for the League Cup winners in England and France. League Cup winners qualify for the Europa League but have to start in an earlier round than primary cup winners.
As why I said usually, I realize France and England get a special accommodation, but to me it seems as if having the league cup winner instead of a team based on league position taking the 3rd Europa League spot opens up the possibility for a bad team to waste a spot in Europe and kill the country's coefficient.
"kill" is too strong a word, but if a country chooses to take that risk, why shouldn't it? On the flip side of your argument is that League Cups still provide a benefit (financial and otherwise) to lower league teams.
Supercups are just a friendly match between top teams. They don't hurt much. League cups are terrible, as they add even more competitive matches to teams. Moreover, I'd reform the national cups to play them in consecutive weekends in August-September, so leagues start in October.