I won't try and argue that having a processor is never the way to go, but I've found that in most car stereo upgrades, unless you're going to spend 5k+ on speakers/sub/amp a processor won't really have a noticeable difference...I'm far from an expert on this, but I have friends who have put put in a processor and it doesn't sound any better than my setup using a sub/amp with passive crossover...When you are only using 2 front speakers as main speakers time alignment doesn't really matter that much...sure you get finer control over frequency and such and a few extra EQ settings, but idk I'm not convinced it's worth it. Feel free to tell me why it is though if I'm missing something.
A processor can be the most important piece in your system. As stated earlier time alignment, phase, and tuning for your car is important. You can drop 5k in just speakers and it will only make a slight difference over stock. I put a little over 1k in my car and it sounded better then people who have just put 2k worth of aftermarket headunit and speakers in. I am an audiophile, I'm an audio engineer, and if you could not hear a difference between a system with a processor and without, then who ever put it in did it wrong. I had the JBL MS-8 and it is an amazing piece for the every day person. Aligned the speakers and gave me a "center" channel which was pretty amazing from that "cheap" of a unit. Also having the 32 band EQ was a must for me because i did tune my car and my sub.