There's a ton of "real medicine" in psychiatry. I'm a pgy-1, doing inpatient this month. so far on inpatient psych, I've successfully bridged a guy on warfarin who was brought in for psych decompensation (he stopped taking his warfarin for three weeks, no acute PE or DVT which would have gone straight to medicine lol). I'm managing someone's chronic pain (discontinuing opiates) in addition to substance dependence. I diagnosed a case of hashimoto's thyroiditis after ordering TSH then TPO antibodies (consulted endo for management). I consult when appropriate and when I don't know what the hell I'm doing. I had another lady with panic attacks in ED sent to psych, checked her tsh it was <.01. I've worked up TBI vs ADHD.
On call you routinely get called for medical stuff, unless it's a code and the person is crashing. Someone fell, you get called. Orthostatic hypotension, you get called. Hypertension, you get called. SIRS, you get called. Somebody trying to leave AMA who's demented/delirious, you get called. At least where I am training, on the psych units you are the primary MD and will get paged about anything medical or psychiatric going on with the patient. You can consult when appropriate and I do, but if I feel like I can handle it, I handle it myself.
A lot of time really sick psych patients only see their psychiatrist so you end up doing a lot of PCP stuff. Plus there's a lot of overlap between mental illness/neurologicla disorders/medical disorders. plus medical disorders can masquerade as psych disorders and vice versa. Don't buy into that stigma that psychiatrists aren't real doctors. We prescribe some of the most dangerous medications in all of medicine: lithium, clozaril, vpa, etc which all have a ton of medical complications that you are responsible to monitor. You wouldn't believe how much **** gets missed on psych patients because they're hard and a lot of ED docs, understandably so, want to get rid of them ASAP. Just because an ED doc cleared someone, does not mean they didn't miss anything.
If you love psych do it, don't not do it because you're afraid of not being a "real doctor" and practicing "real medicine." Yes, you will stigmatized by your non-psych physicians and that's something you'll have to deal with. Psychiatry is an awesome field.