There are many reasons for modding your car, including but not limited to: performance, longevity, safety, vanity, or even just an opportunistic opportunity (e.g. a deal that was just too good to say no to at the time). As long as you enjoy the modding it should be all good.
Regardless of how the car is set-up, I think a safe goal should be to learn how to drive the car- first at your limit, and then at the car's performance limit (in an appropriate setting like HDPE).
Some mods may make this easier or harder to achieve this along the way, but seat time and humility will usually get you there. For example, tracking a loosely sprung, underpowered car will likely force you learn about weight transfer effects faster than driving a tight, light, stiff, powerful monster. Doesn't mean you can't learn in a Cup car, just that its threshold for feedback is higher vs. a 2002. That said, just because you can wring out the 2002 consistently lap after lap, doesn't mean you can replicate that immediately on a Cup car.
Timing yourself for the purpose of measuring your performance is really only relevant once you are driving the car safely at its limit consistently around the racetrack. I understand that different people go to the racetrack for different reasons, but in the HDPE setting learning is generally everyone's primary motivation and timing equipment is a very advanced tool. I've seen relative noobies bring a hot racecar to the track to prep for racing and compare lap times...but while driving the thing superfast, they also blow through flag after flag as they experience dangerous tunnel vision associated with driving too fast/too soon for everone's comfort. You could argue that the timer enables an accelerated learning experience, but I don't think this outweighs the safety compromise of missing flags in any setting.
One of the most interesting skills I have seen on track was seeing how an advanced driver explores and approaches the limit of a new-to-them car. A club racer once took me for a ride in my car and gradually pushed faster and deeper into the corners until the limits of the car were reached, and then he worked to consistently push to just inside those limits lap after lap until the session was complete. Sounds a lot easier then it was, especially with traffic.