I've been using medical syringes to bleed brakes for about as long as I'm in Thailand, which is just over 15 years and they are absolutely the best tool for the job. But you need to have the right medical syringe.
Normal syringe plungers are rubber and that will swell and break when it comes into contact with brake fluid. A nitrile one, which is usually colored blue and not black, can deal with brake fluid. I combine the syringe with a nitrile tube, which you can also get from pharmacies. You can spend a fortune on flashy brake bleeding kits, but this is not only the cheapest solution, it is also the best. Motorcycle brake bleed kits seem to either pop seals or be too fiddly to use – a syringe is simple, effective and cheap.