We do do house calls - I did three yesterday having triaged four more and dealt with them on the phone.
We only visit patients who are genuinely housebound though - always a bone of contention. It takes a lot longer to visit someone than for them to visit us, so if someone goes out to the hairdresser/the shops/Sunday dinner with the family then no, we don't visit unless they are acutely unwell (making them genuinely housebound). I certainly wouldn't expect to visit an 8 year-old at home as on the whole they're pretty portable ime, and if they're so sick they can't come to us they probably need an ambulance.
At the moment GP access is made worse by all the other problems in the NHS. Covid backlog/people who didn't see us then and so really need to see us now. Hospitals are busy so people are discharged prematurely so we spend time clearing all that up. We (in the practice, not me personally) spend hours chasing clinic letters that take weeks to arrive but the patient is requesting the recommended care literally on their way home from the appointment. Discharge summaries with only half the information we need. Patients told one thing and the letter says something else so we need to clarify. We chase hospital appointments to make sure people haven't been forgotten - the last letter we have says they'll be seen in six months and fifteen months later the patients wonders if they've been forgotten. I know one practice locally who have employed a full-time member of staff just to do all the secondary care chasing, which wouldn't need doing if hospital staff had enough time and headspace to do their jobs properly.
We are also managing the huge number of patients who really need to see a specialist, and have indeed been referred, but the wait is over a year and so they come back to us asking for something in the meantime. I don't blame them but I often have nothing more to offer.
I agree with a pp who said that pharmacists aren't used enough. We have a local scheme where we can signpost patients to a booked pharmacy appointment for minor illness but I'm not sure what has gone wrong there - most are simply bounced back to us after a phone call. Doesn't help anyone.
We know we're not doing the best job we can because there is too much work and not enough of us to do it. I promise we're working really hard. As others have said routine days are 12-13hrs and still the work isn't all done. We have streamlined what we can but the demand just far outreaches our supply. None of us enjoy knowing that patients can't get through on the phones, or that people have to wait days or weeks to be seen by us. The decisions we are making are often literally on the basis of who can wait most safely, nothing else. I'm not asking for pity or sympathy, just a realistic recognition that we're not sitting around fiddling while Rome burns.
And so our appointments are full and so other patients go to A+E and so A+E is busier and so people are discharged too early and so they come to see us, and on and on it goes.
I don't know what the solution is, frankly. I don't think the genie can be put back in the bottle, so something radical will need to be done. Whether any government will have the courage or the insight to do this (instead of just rearranging the deckchairs) remains to be seen.