It's surprising to me how often I encounter "decision models" that don't actually include any decisions. I'll answer the question suggested by the title straight away: I think it's a mistake not to include an explicit decision, for reasons that will follow.
Nobody ever wants to admit that their model is a worry analysis, a pointless forecast, an anxiety management device, etc -- they will always say there is a decision. The decision is implicit, of course, can't you see it? This decisionless Monte Carlo risk analysis model is really a go/no-go for the project (Q: what's the hurdle? A: shrug). This valuation model is helping us decide what to bid for the asset (Q: how much less than reservation price do you bid? A: shrug). One can rationalize a decision for almost any analytical exercise.
What do you miss when you leave out the decision? Three things:
1. You're leaving out the most important part, the beacon that guides the analysis. When you have a decision in the model, the "is this good enough" question is about whether you're confident you have found the best alternative. (Yes, you can quantify that in a decision tree.) When you don't, it tends to be about accuracy in the abstract, which may or may not have anything to do with value. I won't get into a discussion of framing, but invisible decisions and poor framing go hand in hand.
2. A decision in the decision tree leads to other fruitful modelling. Often a single decision point is just a simplification of a more flexible resource allocation process -- perhaps we could start the project, observe its progress and make another decision about going to the next level. Decision dynamics can add a lot of value. If you start with zero decisions, it's a big jump to the next one.
3. An explicit decision clarifies the purpose of the analysis with the actual decision makers. The decision review board will be happy to accept a forecast on a subject peripherally related a decision they have to make ("thanks guys, nice graphs!"). But if there is a clear decision -- a decision they have to make -- they're not going to suffer a model which doesn't fit their view of the problem.
Don't skip breakfast, and don't skip the decision. The model doesn't have to be complicated, even a Spetzler Special has a decision, right up at the front of the decision tree where you can see it.