The issue with the Hope Valley line is Northern filling the trains with Manchester - Sheffield passengers with cheap advance tickets (also doesn't help that TPE binned the day return fare). If those services didn't offer a price advantage over the faster EMR/TPE services then they won't be as busy.
(Although I do wonder what percentage of misuse there is with someone buying a Northern only ticket and boarding the front unit of a pair of 185s or even a pair of 170s knowing unless there is revenue or a 2nd guard they won't get caught out)
A good summary.
TPE provide an hourly service between the 2 cities, possibly 6 car 185s but often 3. They offer 1st Class and a catering trolley. On a 3 car the trolley may not be able to get on the train at all let along work along it and in any case you may be almost at your destination if it does. On a 6 car half the train gets no catering.
EMR provide anything from 2 to 6 car 158 or 170s hourly, all what we used to call 2nd Class. There may be catering on these but if 170 only in half the train.
Northern's hourly stoppers are usually 3 car 195s but can be 2, 4, occasionally 5 or very rarely 6. 15x units turn up as 2 or 4 car when 195s aren't available. The effective truth is that Northern's 195 service (taking nearly 80 minutes) is the cheapest '3rd Class' option for through travellers - although 195s are as good for most as 158, 170 or 185s that do the trip in under 55 minutes.
In the same hour a Northern single ticket can be 1/3 that of TPE or EMR. As examples, next Sunday morning prices from Sheffield to Piccadilly range from TPE's 8.09 at £17.30 (limited availability, 6 left in 1st) to Northern's 11.15 at £7.60. All trains currently show as limited availability and will probably show no availability by Saturday. The canny will compare prices from Dore where it can be cheaper, or dearer on those same trains - but by the time you check that may have changed!!
On most days and within some hours those who check will find time flexibility can get them a much cheaper fare.
On the stations along this route only Piccadilly has any regular ticket checking. Some regular users have undoubtedly sussed out how to avoid payment. I've observed them in action. Boarding the front half of a Northern double unit is a favourite. In my recent experience I haven't had my ticket checked on both Northern and EMR services, although the EMRs had every seat taken so maybe others did. My last TPE trip was to Liverpool and my ticket wasn't checked until it was quiet after Piccadilly - very thoroughly too, including my Railcard.
I know some regularly take Promise to Pay tickets from the TVM, their get out of gaol free card! I once saw a large group of walkers being handed such by their walk leader, most of the participants having paid for food and drinks along the way by card!
One reason for the increased passenger numbers being recorded may be that more are buying tickets online. When tickets are checked on the train the inspection will take far less time than it would have done 5-10 years ago. Seeing more tickets being checked is encouraging more to pay.