It's worth to think about it a bit, especially in larger purchases. Significant discounts on the order of 5% to 10% can easily beat all credit card benefits, and not taking advantage of it leaves lots of money on the table.

I have a little lookup table for this. Interest free installments mapped to cash discount necessary to beat the credit card. I just look it up.

   1x -> ~1.9%
   2x -> ~2.3%
   3x -> ~2.8%
   4x -> ~3.2%
   6x -> ~4.0%
   8x -> ~4.9%
  10x -> ~5.7%
  12x -> ~6.6%
  18x -> ~9%
  24x -> ~11-12%

These numbers are actually conservative. There's a lot of credit card benefits that weren't priced in. I add a couple percent to the required discount numbers and round it up to compensate.

   1x ->  4%
   2x ->  5%
   3x ->  5%
   4x ->  6%
   6x ->  7%
   8x ->  7%
  10x ->  8%
  12x ->  9%
  18x -> 12%
  24x -> 14%

Mathematically you are right. However those interest free payments are generally setup in such a way as to make it highly likely you won't pay it off by the end of the interest free period. The bills they send contain the minimum payment - designed to get you past that time. I don't trust my ability to get the fine print right - it only takes messing this up once to destroy all the gains from several times getting it right. So I use the credit card anyway and pay it off every month - that payoff is the one number I can get right every month.