Pre power meter, Strava segments are how I tested my fitness. On days that I was at least somewhat rested I would test myself by doing all out efforts on 1-2 minute climbs (some of my favorites: Bohler, Houston Mill, East Rock Springs). From how I felt on the climb and what the result was, I could tell where and what I needed to work on.
For testing TT efforts, I kept track of what gear I was in on the dumb trainer, always at 90rpm cadence. If the hardest gear I was previously capable of pushing for 20mins felt easy or hard, I could tell where I was at.
Everyone around me said it was necessary to have a power meter to really know how well you are doing. That without it, you really can't tell how well you're riding, or how hard you need to push yourself. So eventually, I got a power meter.
I got a g3 PowerTap hub, which was easy to set up, and simply worked out of the box. At first I swapped it between my TT and road bikes. I did some 20min tests to figure out what my threshold is (more or less). This has been quite useful for training and racing time trials. I don't have to rely on heart rate - which can be deceiving depending on rest, temperature, and many other factors.
However, when using it on my road bike for training rides, group rides or races, I realized I never really looked at the power I was putting out. When the going gets rough, I just hold the wheel in front of me - I don't look at the Garmin. When I'm attacking, I'm going too hard to take the time to look at my Garmin. I don't look at my heart rate either. I just generally don't look at my Garmin unless we're stopped for some reason. This is especially true during races. The only thing I glance at during a race is how much further we have to go.
So, now I only use the power meter on my TT bike. During a time trial, I'm constantly looking at my Garmin, making sure I'm not going too hard or too easy.
"You have a power meter and you don't use it in road races? WHY?!?!"
A big reason, I think, is because I don't care about looking at lots of data.
Don't get me wrong. I log every ride on Strava, and I look back to see some of the main data points from time to time - what was my max/average heart rate? Max/average speed? And, of course, how did I do on any Strava segment I made an effort on?
I've continued my old way of testing my road racing fitness by my hill tests. It just works well for me. I understand that it's useful to know what the number I'm hitting on those hill tests in order to train by zones, so that you know how to judge efforts while training. But I'm not really interested in training that way.
I prefer to train for road racing by feel. So the different types of efforts for me are:
All out sprint, 20-30sec
All out short climb, 1-2min
Hard effort, all sorts of durations
So when I'm thinking through training for a week, I base it off where my fitness should be for the upcoming race, and how fatigued I feel from the previous week. So, for example, if I'm feeling pretty good and the next race is four weeks out, I'll try to do tempo and lots of base pace with some climbing efforts if I feel like it - but no more than 3-5 efforts for the week.
For time trial training, I use the power meter and either try to stay at or above my highest previous number for the duration of the next TT coming up (usually 20min, 30min or 50min for the State TT Championship).
I believe that if I was more regimented, I could reach higher levels of fitness more quickly. But I don't think I'd reach them all that much more quickly, and I really enjoy training by feel. I enjoy the fluidity of it. The only difficult aspect of it is being objective about how I'm feeling in order to avoid overtraining.
So, I think training with a power meter is an excellent idea for most people, and I think that it's pretty crucial for doing time trials. But I think if you're primarily a road racer, you can pretty easily get by without one.