Does the design of a site or app affect how much people are willing to pay for a product?

It certainly can! Usability is a big reason why some companies win a bake-off vs. a competitor. 

The winner gets to say:

"Yeah their product is cheaper, but our design/UI/experience makes users adopt and come in naturally"

"That way you're not buying shelfware"

Premium products need to be premium at every level of the buyer/user's experience. 

1. There are a ton of “intangibles” that we often refer to when talking about what makes a product valuable. A huge factor in this is user experience and the design of a software. In B2B PMM, one of the biggest shifts I’ve seen over the past decade plus is that customers expect the ease and beautiful design of a consumer product at work. I’ve sat on win-loss calls where VPs and c-suite executives say they chose a solution for their team over another because of the design and usability.
2. I’ll also say that design plays a HUGE role in your in-product monetization. The way you work upsells and upgrade experiences into your product without making it overwhelming or a turn off for customers will heavily impact the type of upgrades and monetization you see from your product activity.