If you don't understand the risk difference in taking a gamble on one game (with a one goal lead, so all you have to do is not lose) and expecting two players to make us 15 games unbeaten then I'm not sure how to explain it to you. Both would have led to Europa League qualification, thus millions in return. One is a significantly safer bet than the other. About 15 times safer.
What neither situation would have been, however, is a strategy. They'd both have been a reaction to events at the time, rather than part of a bigger plan. That's where your idea falls to pieces and mine doesn't. In order to get that fifteen game unbeaten run, we'd have been looking at a lot of luck and to be certain of success we'd have needed a left back, a midfielder, a winger, a number ten and a good striker, realistically. In my mind, that type of investment would have won us the league. "Showing nuts" as you simplistically put it would have been a £3-4M investment (at least) in one window. Otherwise, what's the point? If you only do half the investment and lose, how do you bridge the obvious shortfall the following season? You don't. You do a hearts.
You may not like a strategy that says that each season we want to return 70+ points, but that'd be a sound policy. Once you consistently get that then you increase that to 75, then 80+ (that won't be enough even for second place this season). You identify opportunities within the season and react accordingly dependent on the financial situation at the time. I expect a chairman not to tank several million on a whim for very obvious reasons. I certainly don't want the club to be anymore in debt to guys like Milne or Cormack. Where you might have a view on "how to appease the fans", I'm giving a view on a sensible way to run a football club. If you constantly try and appease fans, rather than explain things to them like adults, you'll never have a manager for longer than six months. It's not a chairman's job to appease fans, something hopefully Cormack gets.