Although there are simiilarities between Premium Economy and Business Class, there are some key differences.
"A Premium Economy fare is generally 65% less expensive than a Business Class fare. In terms of space and amenities, these two classes are VERY different with Business Class offering up to 50% more legroom, significantly greater recline, more substantial legrests and headrests, and superior food and wine offerings."
The link below provides a handy table of details-
https://www.seatguru.com/charts/premium_economy.php
But to answer your question, perhaps what might entice customers to pay for the business upgrade is to provide certain discounts to the most loyal frequent fliers of a given airline and allow them to accummulate additional perks or air miles.
From an enterprise/business to business perspective, perhaps airlines can give their corporate customers a bulk introductory discount to get their employees to upgrade and then once everyone's used to it. they'll demand that standard from their employer.

I think to drive more purchases of Premium Economy you have to look at why people might not be buying it:

1. Cost
2. Perception of the value (compared to the cost)

Often people purchasing economy are traveling with families, are low- or medium- level employees, or they work for a thrifty employer. All of these are cost conscious consumers. Also, I think international travel vs regional matters. Personally, I am more likely to pay for a bit more leg room for a very long flight and not likely at all to pay extra on a short flight.
Premium Economy is a hard sell because, as you said, the benefits are not that significant compared to economy and much less compared to Business Class. I agree with Philip Tuet that your best bet would be to offer additional incentives like extra points (maybe 1.5X points for Premium vs Economy) for loyalty customers.
I suspect in the long run Premium Economy will not be a profitable product for airlines. They will either need to charge a higher fare and move all the economy seats to a Premium size, or charge a lesser fare and move all the economy seats to the smaller size. Too many product choices are confusing for consumers and have muddled results, in addition to the costs associated with varied seat footprints.

Agree with the above comments. I feel that Premium Economy is associated with a slight increase in comfort (i.e., additional room, better position on the plane), while Business Class is still associated with a better caliber experience overall. That said, the price differntial is often too significant to justify personal expenditure on Business Class fares -- and many companies that I know of aren't spluring for Business Class anymore. I like the suggestion to offer corporations bulk discounts or extra incentives.

i fly a ton and on flights where I cant get upgraded, the airilines using these premium seats for incremental income from economy class also realize that frequent flyers like me will reserve these seats at no additional cost. We and the airlines know that except on very full flights where the premium disappears upon boarding for standbys that frequent flyers can reserve an aisle seat knowing the other seats will likely be empty, giving them the additional room most desire.
For those who want first or business fir sure, they pay for it. beyond the above, only a few actually pay for premium and they are from economy. It's not the business or first class folks paying so that id not a question.