Lowering team rep and salaries in the SHL fixes this, I've done it in my personal version of the db that I play on. The issue will eventually return as the teams gain rep/budget from year to year, but lowering it helps for a long time. The highest rep SHL teams almost overlap the lowest Rep NHL teams (Arizona 7500, Florida 7500 vs. Frölunda 7000, Färjestad 7000), so players are a lot more likely to want to play there than they should be. You can even sign fringe/aging NHLers in HockeyAllsvenskan if you feel like it (in last year's db Joe Thornton ended his career in HockeyAllsvenskan for me once). Since Mora is a newly promoted team they only have 4500 rep (which is on par with the higher HockeyAllsvenskan teams) but way below the teams that start in the SHL (Skellefteå 6750, Frölunda 7000, Färjestad 7000). When your team is promoted from Allsvenskan to SHL you don't actually gain any real rep or budget increase comparable to the new TV money you get, so it will take you approximately 120 seasons to catch up on budget with the top starting SHL teams as a promoted team. Assuming the salary growth is linear, which it probably isn't. Generally speaking the rep difference when trying to sign an NHLer to the SHL as a promoted team from HockeyAllsvenskan is about 8:1, in the more extreme cases. Benoit Pouliot asked my promoted Mora team for 8M SEK a year to play there, but settled for 1.1M a year with a team that started in the SHL. Also keep in mind that stuff like winning the SHL and participating in the CHL will give the SHL top teams a fair chunk of rep, whereas Florida and Arizona won't likely get much rep as bottom NHL teams, leading to them eventually being leapfrogged by Europe.
Most SHL teams are either running at a loss or are close to running at a loss in real life, purely being propped up by the ~30-35M SEK they get from Canal Digital for TV rights every year. So their budgets for players should essentially across the board never exceed around 30-35M SEK at most, in the 9.6 db the top teams have around 5,000,000 dollars as their budget, when they should be around 3,750,000. When the top teams' Rep is lowered from 7k to around 6k together with their budgets the issue is lessened, and you will still have a lot of actual Swedes in the SHL, rather than having it become NHL-light. The issue with doing this is that it has a knock on effect that essentially leads to you needing to change the rep of every single team in Europe in every playable league and some non-playable ones to get a more realistic experience as far as player movement is concerned (which I did for the 9.4 db, it was so mind-numbing to do). I've yet to try the new "don't make budget adjustments" tick box, but it might fix the Germany issue. Because German teams get in the vague area of 10x as much money as they should based on their database entries as long as their rep is 1000 or higher last I checked, below that rep you can set their budgets yourself (kinda). That did have a slightly negative impact on what player movement looked like in Europe, to say the least.
In my Jets save in 2041 using the changed rep I mentioned above, Frölunda has only managed to creep up to 7150 Rep, and both Florida and Arizona are still chilling at 7500. If this were the 9.6db Frölunda would have 8150 rep to Arizona's and Florida's 7500, which would be an issue. Their player budget has crept up to roughly 4.2M Dollars, which means they still have less buying power for NHL players than they do at startup in 9.6. So unless you plan on playing a really, really long save those proposed changes essentially fix the issue. The team that started in HockeyAllsvenskan who spent the most seasons in the SHL in that save was Leksand, who spent 17 seasons in the SHL (this was on the 15/16 db btw) and with a budget of 6M SEK, after 17 years in the SHL being paid 30M SEK a year for TV rights their budget has risen to 12.1M SEK, and their rep has climbed from 4000 to 4570, so less than the lowest starting team in the SHL, which was Karlskoga/Malmö/Rögle at 4750 and that budget is essentially that of a 1st year promoted team in the SHL IRL. So although you can be promoted from one league to another in this game, there are no mechanics to actually make it function in any remotely realistic way.
Most SHL teams in 2041 are primarily made up of Swedish players with anywhere between 5 and no American/Canadian guys who legitimately didn't make it in the NHL. No big names that shouldn't be there, they even have one of my old 3rd rounders that just missed making my 4th line and ended up going to Frölunda instead, so the exact kind of guy you'd expect to find in the SHL.
Meanwhile in another save that I did pre-editing (again this is last year's db. But the rep and budget values from last year to this year haven't changed much if at all) when we look into the Rögle camp in 2025 we can play a game of "name that top 6 NHLer":

Sure they are all in their mid 30's or older, but do you think a mid 30's Lucic will play in Rögle?
So there is an issue, and it is really easy although slightly time-consuming to fix. The lower a league you play in the more obvious it gets, like having ballpark 3k rep in Suomi-Sarja being able to sign ex-SHL players to amateur deals. Or being able to sign 50k $ players for free in the lowest playable tier of British hockey on amateur deals. Both things are quite possible with the rep and salary values as they currently are, which somewhat defeats the purpose of making sure the European rosters are correct, as the AI will instantly go out and spend all their money on replacing their entire core. Making your hard work on roster research somewhat pointless, so fixing this should probably be a priority since it's a super quick and easy fix. I've already had to do it three times myself in the last year (8.2, 9.1, 9.4), and I'm an idiot who doesn't know how to mass edit so I do it one team at the time in the editor and still had it done in less than 3 hours. Oh, and while we're on the subject; Who gave Borås 4000 rep and 750,000$? That's just silly!