If you get 4 new cards a year and only use the cards in order to meet the minimum spend, it could be worth it. But it really depends on what cards your getting, how much the bonus is, and what you plan/hope to do with the money.

For example, let's say there is a card with a 50,000 point bonus for a 4K spend in 3 months. Let's further say that each point is worth 1 cent if redeemed for cash (more if you use it for travel) so that the bonus is worth at least $500. If your normal spend on the card could generate $1K a month (3K in 3 months) then charging one month's rent for $40 is totally worth it.

But it's a math problem and you haven't given us enough info.