Do product reviews actually increase sales?

Yes, and the effect is largest on items people are uncertain about — fit, quality, size. On a commodity with a known brand they change almost nothing.

The reasoning

What matters more than the average score is the number and the recency. A 4.3 across two hundred recent reviews outperforms a perfect 5.0 across six, because the second reads as either luck or curation.

What most people get wrong

Discounting to grow trains customers to wait for discounts. It works once and costs afterwards.

Traffic is the expensive problem and conversion is the cheap one. Doubling a 1% conversion rate is usually easier than doubling visitors, and costs nothing per month.

Retention beats acquisition on every measure, and almost every store spends the other way round.

How an app changes it

Push notifications are the one growth channel you do not rent. Every other route to a customer is paid for again each time.