Personally, I find the signup bonuses worth it. I've fallen a bit out of the game recently (since moving to Canada) but I'm dipping my toe back in. Basically, we'd sign up for cards (typically with the first year annual fee waived), get the bonus after a couple of months, and repeat. With a spouse, we'd go through maybe 5 or 6 cards a year. Some of our favorites were SouthWest, Chase Ultimate Rewards and IHG.
And, rather than cancel cards, we'd typically just downgrade them to something with no annual fee.
It's a bit of time, but not very much. Maybe a couple of hours a year?