It was called transpirational cooling and it would have required 50kg/s of coolant for 5+ minutes of reentry heating i.e. 15 000 kg of spare methane or water which acts as dead weight that could have been payload. An ablative heat shield literally weighs half that at least not counting the transpirational piping and pumps and sensors .etc that balloon the 15 tons even higher.

There's a reason NASA and the USSR never seriously considered actively cooled heat shields and instead let ablation do the cooling.