I keep my budget on a spreadsheet. I can log into my bank and view my savings, checking, and retirement accounts, as well as my loans. Why would I want to expend the (seemingly significant) extra effort and use financial software?
It comes down to the resolution you want to have on your personal finances. A package like GNUCash allows you to easily answer questions like "Exactly how much do I spend on interest per month/year/decade." Same with pretty much any other expense, liability or asset you have whether it be taxes, utilities, your home equity or your net worth. The other tools you mention are nice, and certainly convenient, but they tend to lump things together in broad strokes and omit many categories altogether (taxes). Ultimately by having such a fine grained accounting tool, you can target small or large things to better budget your money.
Another thing a package like GNUCash provides is a single, private place to consolidate all of your finances. This is nice for things like net worth and asset accounts that you might not want to give a company access to.
Finally, GNUcash in particular helps normal people think like accountants. Rather than lump everything into 'income' and 'expenses', once you start using GNUCash you'll start thinking in terms of equity, liabilities, net-worth and assets in addition to income and expenses. This gives me a much more accurate view of my finances and helps me better target areas for improvement. In short, it helps me to see the broader picture which helps me to keep my eye on the prize - which of course is to not have to worry about money at all.
As asked previous in the week, there is a big difference between budgeting and expense tracking. Using software, like GNUCash, allows one to track their spending. A budget is a plan, the tracking is what actually happened.
I do not track expenses, although I do budget. For me, hitting financial goals is good enough of a track, without investing the time and energy into tracking every penny. One could easily criticize my method, as how can you have a good plan without continuous feedback?
For me it is an example of the 80/20 principle. If I put in 20% effort into making and sticking to a budget, I will obtain 80% of the financial success that a person who devotes 100% effort into budgeting and tracking. A person with the same income and life events, who budgets and tracks, will likely be more successful that I, however, not overwhelmingly so. For me time is better spent on other endeavors.
You seem to have this attitude as well, but those that do track have it as part of their path to financial success and probably view us as somewhat foolish.
This is another example how personal finance is more about behavior than math.