Almost every shonen anime/manga seemed to have a goal relating to the main character wanting to become the best whatever compare to everybody else. Its been done to death; even in mangas I like including One Piece, My Hero Academia and even Death Note.
1) Those would be classified as Seinen. Especially One Punch Man
2) One Punch Man is actually the reversal of the Best of Best plot. In this case, Saitama is the strongest hero around looking for a challenge that would kick his ass.
3) There are examples of Shonens that don't do the Best of Best plot like Ruroni Kenshin (which is very similar to Trigun), JoJo's Bizarre Adventures (save for maybe Part 5), Dr. Slump, YuYu Hakusho, Hunter x Hunter, Baki (which actually deconstructed such goal), Fist of the North Star, Devilman, etc.
Bingo. Even though its not a typical fighting anime like other contemporary animes, Death Note is still a (rather twisted) Shonen anime that follows the usual tropes associated with them.
And the whole goal of making Kira a symbol of justice/god of the new world really fits the moniker of becoming the strongest in the world goal; except if the main character of the story is actually the villain.
Pacing is definitely an issue that needs to be worked on. This is why I don't watch much long shonen like Naruto and One Piece when the manga is a much quicker and better experience. Another is today's protagonists looking back at characters like Deku, Asta, Tanjiro, etc the're all similar in being bland characters with no depth not to mention stupid things like Astas goal being a complete ripoff from Narutos or Dekus need to cry in every situation. That's why characters like Denji from Chainsaw man is a breath of fresh air. These are a few things shonens need to work on.
For me its the broken power systems, the writers need to establish the power levels certain characters can reach, also id like to see the characters actually do bonafide training, even if its just one episode of training it adds credibility. Also if the romance is not going to be achieved or made satisfying by the end, whats even the point of having nay romance in a shonen anime at all.
There are plenty of shonen including training. Yu Yu Hakusho, Hunter x Hunter, Jojo's, Bleach, and Naruto being examples. You might want to just stick with older shonen as plenty contain these elements.
For me, look at what "Kill La Kill" or the first two story arcs for JoJo's Bizarre Adventure did. Then look at something like JoJo's third story arc (Stardust Crusaders) and don't do that.
-Don't waste my time. That is the biggest thing that kills me watching a shonen anime. Six episodes running at about 24 minutes is over a movie length long and I'm expecting something meaningful to happen. If plot is at a near standstill with nothing new, then the people behind the story need to learn to cut some stuff out. --Related to the above, but I'm under the belief that any fight going over a single episode better be epic. And not in terms of flashy scenes, but the fight that has been built up for a long time. I don't want to watch JoJo fight some enemy stand that takes two episodes when in reality it could have been condensed to one as it feels like it takes forever for them to even get to Egypt. Not to mention that most of the stand users are pretty easy to understand and the episodes are just padded out with people talking about crap we don't care about. Meanwhile, the finale for JoJo 2 does a great job with each episode ending up changing the dynamics of the fight to something new instead of just two people trying to punch each other and screaming for so long. --And no flashbacks in the middle of freakin' fights. Good grief, that's just stupid padding. --I have mixed feelings about beach episodes and the like. I'm generally not fond of them but I have seen good takes on it as they show me more of the setting or characters. --Same with filler episodes. If it adds nothing, drop them. I get prior that this was to wait for new chapters to come out in the manga. But they end up being annoying for me. Funny enough, Bleach had a filler season that I thought was pretty good simply because it was episodes showing off character's weapon's personas and them having plots dedicated to them. (It also helps that they did it at a point where there wasn't this massive thing we needed to worry about...I think.)
-Recap episodes need to be done much smarter. Kill La Kill is a bit extreme by stuffing the entire recap in about two minutes at the beginning of an actual episode. The best one I've seen though is Avatar: the Last Airbender where the recap episode is done by a play that the group watches and comments on. Said play even pokes fun at the group and might have ended with a cliffhanger for the next episode.
-Tournament arcs need to be dropped or sped up. They're all pretty boring after a while and have been done to death.
-Battles need less "power rating" and more about different kinds of fights. This is something that One Piece did good at: battles could end up being anything thanks to the existence of Devil Fruit Powers. So instead of having enemies that could just hit harder and harder that the characters need to keep up, they could have powers that are more and more difficult to deal with in certain situations. Even outside of that, you had normal people who were just really good at fighting or were a species that was dangerous. (Too bad that battles tended to drag on forever.)
-Keep it simple with the powers. Bleach did a lot of things right but this is where it dived bombed. Ichigo is a human that can turn into a Soul Reaper due to odd circumstances. Due to those circumstances, he also develops hollow powers to become a soul reaper again. So compared to others, he fights more recklessly and with emotion. But he is the special snowflake that is falling with special snowflakes because all of the captains in the Soul Reaper society have unique powers with the head still being the most powerful. That right there would have been great. Instead, Ichigo's dad turns out to be a Soul Reaper who took human form and had children with a Quincy, meaning that Ichigo has Quincy powers on top of his hollow-soul reaper powers. And he has extra powers as well because...honestly, I forgot as it was getting ridiculous. Compare this to something like One Piece, where Luffy just has this one Devil Fruit Power and sure does act like the previous King of the Pirates, but that seems to only make people think he might actually have a chance of becoming the next King of the Pirates.
-Finally (among those that I typically see at least,) actually have a good story. This is what murdered Fairy Tail and Sword Art Online for me. Fairy Tail felt like I was watching something from a previous anime that in the first episode alone, I was naming off other shows that it reminded me of, all the while not having anything that stood out to me. Sword Art Online had so many details that made me think that the person who wrote the script had never played an MMO and that they had no idea how game development even worked.