When I'm playing the session, I keep going back to the unconventional approach of "earheads" since the late 80s, where what is normally overheads is instead attempting to replicate what the drummer hears, and typical overheads sound nothing like that because the drummer literally isn't floating over the kit, which sounds way different compared to the throne position. In other words, the "overheads" are spaced and just above ear level, maybe 12 - 16" away from each ear, facing low-height cymbals.
But like anything, there are always compromises. The cymbals in this case are quite low and relatively close to the toms so that the overheads are still picking up the bulk of cymbal wash when they are teetering back and forth on the stands after being struck. Too low, and the cymbal sound would quickly fade in and out too much. SDC omnis help with this, however, which is what I typically go with. But sometimes I'll go for ribbons or LDCs depending on the material.
In this setup, the snare is centered in the image, but the kick is off to the right. I measure each mic from the snare within 10 mm or less. However, the kick ends up being centered at mixdown due to the balance of the kick mic being relatively higher than the other spot mics. Never a problem for me.
Also, the susceptibility of hitting the overheads could be much higher, depending on the drummer. Definitely a downside, especially if you're using high end, expensive, or rare mics.
For me, the advantages outweigh the disadvantages. The end result always sounds closer to how the kit actually sounds to the drummer (and the audience; the audience isn't above the kit, either). The cymbals sound much closer to the way I hear them in real life, and that's because the mics are picking them up the way you hear them in real life; mostly from the side and not from above. Of course most of a cymbal's brightness radiates from its edges, and its mids and "honkiness" will come from above the cymbal.
I also find it as the best method of balancing my kit evenly while listening to only the overheads through IEMs during tracking and practicing, or rehearsing. In addition, I very rarely, if ever, need a hi hat spot mic with this method, as long as I (and potentially another drummer) balances all the kit elements well. To me, the hi hat mic never sounds nearly as natural as the overheads in this case, and it doesn't matter what hi hat mic is used; I have over 50 to choose from. That said, for some drummers and hi hats, they may end up being too loud but that's never been a problem for me.