Not all low cost pickups are bad but no-name pickups that come in the majority of guitars under $500 are normally very poor quality. Pickups with poor quality and materials introduce unwanted frequency boosts while also not being made to enhance the frequencies you actually do want.
When the poor quality hits the amp or a boost pedal then the amp, you are boosting, distorting and compressing a bad signal from the poor quality pickups. In a live rig you factor in the volume and feedback etc whereas in a home studio with an amp sim you have to factor in the additional unwanted digital frequency boosts due to your interface, computer and so on.
Another myth in pickups is that you need high output pickups for hi-gain uses and genres. I once had this belief until I saw the light of middle output pickups in the 9k area. PAF style pickups in that range can do literally anything. It’s better to need to boost a lower output and cleaner signal because then you can increase as you want to rather than being stuck with a really hot signal. You can also do more with a middle output pickup genre wise so the pickups become way more versatile.
Guitarists on a budget have many options but it really boils down to a few. First you can go on Reverb to find a ton of used pickups being sold for next to nothing in decent shape. Just be sure there’s plenty of wire left on the pickup. The next option would be to buy cost effective pickups from a quality source like IronGear pickups for starters but then you also have GFS from Guitarfetish or Guitarheads pickups which are a great bang for the buck. You can also save a lot of money by buying yourself a decent soldering set up and learning how to do your own wiring.
When tone chasing, there may be a certain pickup responsible for some of the key characteristics of the tone. Humbuckers, single coils, P90, lipstick and other pickup types have very different tones and abilities so it’s kind of important for guitarists to know their stuff when it comes to pickups. Always do your research.
Bass pickups are no different than guitar pickups in the sense that they matter just as much. I can’t tell you how many hours I have wasted cleaning up or trying to process a signal from a bass with bad pickups. If you a re going to spend money on recording, make sure you have decent instruments with good pickups.
If you shop and buy smart, learn how to do your own wiring and handle your own repairs, you can try tons of different pickups or pickup combinations without breaking the bank. We will be coming up with a simplistic pickup / genre / use guide shortly.