The Amiga 500 does have built in colour output, in the form of RGB analogue video. This is similar to VGA (although at TV video frequency) as used by most computers to attach to monitors in the pre-digital interconnect era. Your TV may not have RGB video input but just about every TV in Europe does in the form of a SCART connector. For Televisions with SCART only a few resistors are required to build a video lead
with excellent picture quality. Please do not recommend the use of the video modulator to those that don't require it. Your problem with sound over RF could be due to the wrong type of modulator as PAL has many variants that have different sound carrier spacing.
The mono composite video output built in to the A500 is there to allow use of a high persistence monochrome monitor with interlace video modes for reduced flicker.