I'm guessing there is a staff rota and it's only done in 1 month in advance and therefor booking appointments outside of this would result in cancelled appointments, which is something cqc would call them out for.
Working in social care for 11 years has taught me that while people day to day care and try their best. The ultimate management of people is all about ensuring things look(look being the key word) safe and effective and caring. Sure in your situation it looks uncaring, but the systems set up to meet its own objectives. What's inpractical for you, looks good to the people at the top.
Is it set up like that on purpose? Probably not.
Sometimes I feel like my three year wait is some ploy by the clinic to make sure I can't reach treatment by a event happening in those years that would result in discharge for example a letter goes missing or suicide/death or mental health issues, basicly any event that could mean I'm not on their listwhich could prevent me from receiving treatment. The reality however is that the system is just set up to meet people's needs with the resources available. In my case the resources are limited. Does it factor in people's lives and individual needs? Not unless those needs are stated in a care plan or in notes.