I'm thinking about changing insurance provider and maybe switching to the Hausarzt model, but I'm unsure how this would work. Would I have to get re-refered by my doctor? Would they have to sign something on an ongoing basis to get my treatment covered? Because that would be a real hassle.
Currently I have the standard insurance model and I see a psychotherapist around once a month, with occasional prescriptions from the psychiatrist.
Your GP needs to write a ‘Bon de delegation’ ( no idea what ît’s called in German) referring you to the named doctor and it will be covered by the insurance. My GP does it for the year each year for the specialists I have to see regularly for my ongoing treatment.
The Hausarzt-Modell means that every step you take, for anything medical (with the possible exception of gynaecology) must first be presented to your GP (Hausarzt), who will then decide on whether you should be getting treatment and, if so, will refer you to a specialist. Often, these specialists are on the GP's list (or the list given to the GP by the medical insurance (Krankenkasse). After all, that's their way of trying to reduce costs, which is why the premiums with Hausarzt-Model are lower than those with free choice.
OP, if you are already working with medical practitioners you like and trust, then it's worth checking first with your GP whether or not he/she would willingly continue to refer you to those same practitioners, especially if they're not on their preferred list. Some GPs working within the Hausarzt-Modell will agree to refer the patient to other specialists whom the patient has chosen, but some refuse.
The kind of arrangement that Belgianmum describes sounds very good, and that's exactly the way it should be. It works for as long as one has a relationship of trust with that particular GP. Therefore, when considering reducing your freedom of choice of practitioners, by instead submitting to having everything first assessed and prescribed by your GP, it's also worth considering what you would do if that particular GP left/retired, etc.
If you have a good relationship with your therapist, consider it priceless.
I have a Hausartz model and it has never been a problem, even when referrals aren't perfect. When it came to therapists, the GP referred me to one who was not a good match, and when I said as much, they were very understanding and asked if I wanted to find one myself or to have them do more research on fluent English-speakers referral. There was no short list to choose from -- they can literally refer you to any specialist with the appropriate license and they would be covered. My OBGYN (you never need a referral for OBGYNs if you need to see one) also gave me a referral to a therapist after this, and that therapist gave me a referral to her colleague, who was an excellent match and whom I continue to see. All in all, the process was not difficult at all -- everyone involved seemed really focused on making sure I got the care I needed AND felt comfortable with. Both language needs and personality needs were taken into account.
I have a number of specialists I see annually, and it has never been a problem to get referrals -- I only had to get referred once to a specialist to see them on an ongoing basis (for example, annual dermatology appointment only had to be referred once and can now go until the dermatologist determines there no longer a need for recurring appointments or additional follow up).
My advice would be to speak with your therapist about whether they can refer you to themselves (this would be a reference on file from your doctor that is currently covered and could suffice). If they can't, call/e-mail your GP and ask if they'll refer you -- across my experiences, doctors have been super helpful here and there would be no reason for the GP to not to refer you in the case you describe.
The lower costs, from my understanding, come from having the GP catch many more problems that they can treat (cheaper than a specialist) before referring you. Again, in my experience, GPs have no intention of gate-keeping in cases where they don't feel like they're the right person to address/monitor the issue/recovery.