Probably my worst navigation blunder ever involved me blindly following the CDI straight from a station along an airway. Didn't lose the signal initially... what it did was simply start lying to me as I got farther away. Beware of that. Terrain, distance, etc, etc can all influence VOR signals, even when you have a good "to/from" indication.
Had I done the wiser thing- focused more on what time I should arrive at a given waypoint (which is the heart of dead reckoning) than on the needle, or even the fairly unvaried terrain ( a limitation of pilotage), I'd have caught my error sooner.
So FWIW, I think a good exercise would be to plan a leg along a radial, but use the station passage (or DME fix, or intersection, or any point on a radial) only to confirm that you chose the best wind correction angle, visual landmark on the horizon, etc. Don't rely on, or chase, the CDI.
Another thing to make more productive use of VORs without letting your DR and pilotage skills wither is to think of VORs first and foremost as tools for plotting your position, not as directional beacons. Radials usually work fine for course tracking, but only when the right heading is chosen by the pilot.
I've made very good progress along DR courses by using VOR radials to create fixes ... you still have to use DR and pilotage, but the VOR is there to back that stuff up. Also very handy for getting "unlost", or for creating a specific time at which you should see that destination airport, even if the VOR station is not on the field. Or for defining airspace boundaries... radials can be very handy for that, and I don't mean using DME.
But it should be noted that I got out of the mess mentioned earlier with pilotage alone...