The original question asked about complete turnkey systems, without "any electronic modifications, like using tools and modifying electric components", for which the other answer provides solutions. This is the answer for all other possibilities, as prompted by Aziraphale:
It might be that third party producers provide remote controls ready for implementation in LEGO sets. We see the same for lighting systems that contain LEDs, batteries, ultra-thin wires etc. I would also accept non-professional custom solutions that allow usage of non-LEGO parts in my sets, possibly by showing how to glue/connect non-LEGO equipment to LEGO bricks.
Disclaimer: I have neither authored, nor tested any of these ideas, but I have reviewed them all and deemed them useful and correct. The information contained them might nonetheless be incorrect, outdated or unusable for any other reasons.
The simplest option would be to extend the range of the existing receiver by increasing the power emitted by the IR remote control, by using a custom IR transmitter:
A fully LEGO compatible DIY electronics project is authored by w4ilun and uses a Toshiba motor controller embedded in a custom-designed printed circuit board to interface with cut and repurposed PF cables:
If we are willing to forego LEGO Power Function motors as well, we can use any kind of DC motor we can build a LEGO compatible enclosure for. This project uses the radio control parts salvaged from a toy car to integrate them into a LEGO chassis:
Or an existing 2.4 GHz remote can be used with this custom designed receiver: