While I agree with the sentiment I think you're putting the blame at the wrong door.
Everton don't have the luxury of being able to go out and buy World stars. So they either need to get them before they become household names, or get players further down the pecking order.
Of the star quality players you mentioned -
Stones was brought in by Moyes and took a while to be considered a good signing for a top club. He was persuaded to stay an extra season by the club so he was never a possibility for Koeman, he was going before Koeman even arrived.
Lukaku - was surplus to requirements at Chelsea, highly promising but no big clubs came in for him. Even when he was banging them in for us, it wasn't til this Summer after he said he was leaving (tapped up). I've seen it said that he too was persuaded to stay for another year.
Deulofeu -
at him being considered a top player. But Barcelona executed a buy-back clause which was put in before Koeman even joined. Everton couldn't have stopped it if they wanted to.
Barkley - still an Everton player, and I guess his situation is slightly different. Not sure what his deal is, has he fallen out with the manager who got the best out of him? Or does he just want a bigger club to play for. Perhaps he's been badly advised, or maybe he's realised that his media profile is very poor and a move to Spurs would solve that and get him straight in to the England side.
The point though is that none of those 4 players were coveted by top clubs when Everton first signed them. It was the platform that Everton gave them that helped them get to that level. You're saying that none of the current squad are at a top four level, and I agree. But given time, Tom Davies, DCL, Michael Keane and Pickford all have the potential to jib us off for apparent 'bigger and better things' further down the line. As a club, previous manager's should have already had a succession plan in place for those kind of players leaving. Is this why Walsh has been brought in? To ensure that.
Everyone could see we needed leaders, so they sort of went out and tried to bring some in with Williams, Klaasen, Sigurdsson , Rooney etc. I personally think all 4 are a waste of money. For me the transfer business was disjointed, it's like a box ticking exercise - leader? premiership experience? media profile? Koeman stated publicly on numerous occasions that he wanted - and had told the board - a left sided defender and a striker. That suggests to me that he wasn't in charge of the transfer dealings. Sure it sounded like he had a say in them, but he wasn't the one making the decisions.
I've said previously a lack of a striker/goalscorer in games, means we have to work too hard to score goals. This puts pressure on the players from the start, they know they can't make mistakes, as it's unlikely we'll score many goals. This is Everton this season. We tend to start games ok and put pressure on for the first 10-20 mins, but when that goal doesn't come the nervousness sets in, you really have to score when you're on top, and that nervousness spreads right throughout the side (and crowd) and the safety first approach produces dire performances.
Koeman is the figurehead and as such I can see why he's taking the blame from most people, but the problem is deeper than that and I personally think he'll turn it around (with help in January) and I'd be surprised if we finished too far off 7th place come the end of the season.