I've noticed the huge amount of free games for this spring sale, and that's awesome.

I've added most of them in the cart, and now whenever I try to checkout I get an error.

Is that because I have too many games in the cart, or because the checkout server is overloaded anyway?

I'll rephrase: will removing items from the cart, trying a smaller checkout, improve the chances of it working, or is it irrelevant?

Please only answer if you know it, random guesses aren't really useful. Thank you for understanding.

It's irrelevant. Try to restart your browser maybe and do it again.

Instead it was just that.

I've removed all of them save from 8, and the checkout page worked.

Most likely you had a free DLC in the shopping cart that you don't own the base game of. Checkout is not possible in that case.

The other option being an item or more added that you already have. Then only buying as a gift code is possible.