Yes, but there's also a downside to raise interest in a economy that's down on its GDP goals. We should have raised interest rates, taxes, and cut spending in 2004-2007 but failed. Overcompensating for those mistakes now isn't helpful.
You summed up my political/economic policy in one sentence. If you cut taxes to stimulate a weak economy then you should raise them when when speculative bubbles start popping up. We should have raised taxes higher in the nineties as well. I would rather have seen that money go to pay the debt than go into the pets.com IPO.
It's more complex than that though, right? If you raise taxes in 1997, you're going to stifle both bad investments like Pets.com and good investments like broadband infrastructure. You also have to choose between reducing the national debt and spending. In hindsight, maybe we should have used the government surplus to build infrastructure or improve our healthcare system.
Reducing the national debt too much is another thing to worry about. Our financial system requires a good number of treasury bonds. Tons of players in the financial system need to have that specific kind of asset on their books.
Also, just as a matter of theory: If a government project will create a net tax revenue increase in the future through new economic activity, above the cost of borrowing, why not deficit spend on that project even in good times?