That depends on how much time and how much money one has, doesn't it?
I suppose that time quickly becomes the more limited and precious of the two so the more money available the less time you're probably willing to spend solving problems yourself unless you think it is critical for you to be involved.
That's how it tends to work, doesn't it? People DIY to save money for instance, it can be a choice but if you're skint then it is a necessity. Or, you're bootstrapping your business and you do about everything yourself because you have no money to hire.
And if there is no money and time required is prohibitive then it does not get solved at all.
I look at what it will cost by paying for it. Then evaluate how much many hours it would take to do it and what my current hourly rate is. As the cost becomes cheaper, consider paying. As the cost becomes more expensive, consider doing it.
As you say, when either time or money would be effective to begin with, regardless, the mere expenditure of money alone more often results in temporary solutions to permanent problems.
You spend money, it gets done quicker (sometimes, but that’s the intent) but if it’s not the right thing, it’s a waste.
You spend time, you have time to adapt and adjust, but you can be too late.
I’m moving towards smaller, cheaper, and faster incremental interventions. Accrete successes, scrape off failures.