First of all, pretension is a more bookish term, so it would not surprisingly show up more in books. That does not mean it shows up more in speech or casual writing (especially online writing). Second, pretentiousness is a noun made from the adjective pretentious, which virtually everyone knows and understands.

What the meaning of pretensions?

1 : an allegation of doubtful value : pretext. 2 : a claim or an effort to establish a claim. 3 : a claim or right to attention or honor because of merit. 4 : an aspiration or intention that may or may not reach fulfillment has serious literary pretensions. 5 : vanity, pretentiousness.

What does have no pretensions mean?

DEFINITIONS1. a way of behaving that is intended to impress other people but seems false or too deliberate. There's a refreshing lack of pretension about her.