What is shown on that approach isn't that a straight-in approach to the runway isn't allowed, but rather that there are no straight-in minimums published for that approach.
Why they didn't publish straight-in minima is beyond what I can tell from the chart, although the combination of obstacles near the final and reduced navaid accuracy so close to the VOR seems plausible. ("Didn't feel like it because runway 7 is rarely in use" seems less plausible: once the approach has been constructed, most of the work is done, so adding straight-in mins would be negligible extra work at that point, if the criteria were to allow for them.)
The obvious difference between the VOR approach and the GNSS approach is the allowed altitude you can descend to inside of 3 miles to the runway; a precise final approach course definition (i.e. using GNSS) would allow a narrower obstacle clearance corridor - so when you're on course there are no obstacles reaching to within XX feet vertically for YY feet laterally. The less precise guidance from the VOR probably requires a wider corridor, so if some obstacle to the side of the final intrudes on the wide corridor, its minimums have to be raised to clear the obstacle vertically. Raise them high enough, and the straight-in becomes impractical, so only circling mins are published.
Note that if you got the runway in sight & could make a safe approach and landing using normal rates of descent, you could land straight-in from a circling approach. The key point would be that below the circling MDA, obstacle clearance is no longer provided by the approach and it is the pilot's responsibility to avoid all obstacles visually.