Manchester City and Real Madrid always give a lot of importance to their domestic league and Champions League but we don't see that in case of Arsenal. Arsenal may take the English Premier League tournament very seriously but they are not too interested in the Champions League tournament. If they had given more importance to the Champions League tournament, their performances in the Champions League would not have been so bad on a regular basis, while in the English Premier League they are rightly second in the points table. Real Madrid and Manchester City are as much expected in the Champions League as we are in Arsenal, so Arsenal should prepare for the Champions League and prepare accordingly.
Real Madrid will certainly be ahead of the rest of the teams next season with the way the teams have been so far and Manchester City could do well there as well but Arsenal have yet to change their squad so it wouldn't be a surprise if their performance is similar to last season.
I think you're honestly wrong, in my opinion Real Madrid gives more importance to the Champions League, in fact the season in which Barcelona won (two years ago) they actually abandoned La Liga to focus on the Champions League. I don't know about Manchester City, but for Real Madrid the priority is the Champions League.
It doesn't matter whether Real Madrid prioritize the Champions League or La Liga because after all, Real Madrid always have a big chance to get trophies every season. So, I think when Real Madrid failed to get the La Liga trophy but managed to get the Champions League trophy, I believe it also does not guarantee that Real Madrid prioritizes the Champions League more than La Liga. Because anyway, when Real Madrid failed to get the La Liga trophy also the fact that Real Madrid still made efforts to catch up at that time, but the results were still lost.
So yes, I personally believe that Real Madrid always has a very good chance of getting the trophy every season because after all, Real Madrid really has an advantage in all aspects compared to other teams. But even though I believe that, at least I also still recognize that failure can still occur, because every competition will certainly have a team that wins and a team that loses.