The biggest reason your cheap Tele sounds poor is due to the use of ceramic magnets and steel pole pieces in the pickups. Even in middle of the road Teles you can find such pickups sometimes. These pickups are not made to sound good. They're made to make noise and save money. No Tele pickup was made this way in the early days when they were first designed, they were designed to sound good, with alnico rod magnets.
These pickups are made with alnico 5 on the bass strings for a bright, tight and cutting bass end response without flub, and alnico 2 on the treble strings for a warmer, less clinical and more singing top end. You get a beautiful mix of warmth on the top end and sting on a bass end with the hybrid magnets.
Here's a set of Tele pickups with alnico magnets. These sit nicely between the ceramic rubbish that you can find stock in many Teles and boutique offerings (such as our exclusive Alegree pickups). These use high end components, but are machine wound to a rough spec. You'll get yourself 70% of the way to a boutique offering for a fraction of the price.
The specs (neck/bridge):
Resistance: 8.5k/7k (different gauges of wire are used - this doesn't mean the neck is more powerful)
Magnets: Alnico 5 rods on the bottom three strings and alnico 2 rods on the top three strings
Copper plated steel baseplate (a ferrous baseplate is a VERY important component of Tele bridge pickup tone that many pickups in this price range lack)
Chrome plated brass neck cover (vintage material)
Cloth covered output wires
Supplied with mounting screws & springs.