Cutting cards up immediately after meeting minimum spend often doesn't meet the requirements. Consider the BA 100K offer through Chase. 6 months minimum was in the terms. And many later received offers to earn 5K miles for minimum spend over 3 months - some got this offer more than once. You'd have to request a replacement card then.

What to track? Annual renewal date - that's when you should either close the account or try to get the fee waived / get retention bonus. Then dump the card a month after that. Keeping cards is beneficial if you use it to keep various program miles from expiring (assuming you also get the fee waived and/or a retention bonus every year to make it worth keeping).