Whilst not wanting to take the sheen off Forest's European success one bit, they achieved their wins when it was achievable for a club of their size and stature to do so. It was great for them but there's no hope of that happening now. The cards are stacked very much in favour of the big clubs. The European Cup giving way to the Champions League and the PL breakaway in the 1990s and 'Project Big Picture' and the ESL movements more recently show that those pulling the strings want a less egalitarian league structure and to make life that little bit easier for the 'big' clubs. There's a cabal of clubs - well, billionaire club owners - who simply don't want to see anyone 'do a Leicester' ever again because it encroaches on 'their' turf.
Your point about it being an impossible legacy is a good one though. It's just about recent enough to still be in many fans' memories but starting to fade away away as the current two or even three generations of Forest fans take their place who have known nothing but second (and third) tier football. The Championship is a beast of a division. Money is thrown around at a ridiculous level to get to the untold wealth of the PL - £15k a week is the average Championship salary for a player - so many are paying way over the odds to get there. Some like Millwall and Barnsley are happy to tread water as they don't have the clout to go much further, not Forest still cling to the idea that they can be a PL club and the culture of desperation to get there has seen this ludicrous managerial firing and hiring policy.
It's one of the reasons why I'm quite content in League 1. Seven 'new' teams to play each season, the EFL Trophy for the youth/development teams, decent enough football and without a carrot of the PL in place it means we largely spend without our means. Of course I'd take promotion but I wouldn't want us trying to go toe-to-toe with the big players if it any way jeopardised the club. We've been there before in recent memory and I don't fancy dusting off any FOUL letterheads any time soon.