The word "blame" was nowhere in there. I am suggesting that the parent ask the teacher about what the child should be doing during the holidays. I think I used the word "responsibility". If part of the learning process involves doing things between lessons, then the teacher must consider this. I am writing this as a teacher.
Sorry, but it makes not the slightest difference whether you literally used the word yourself, when you wrote:
They consist of the work the student does in between plus the lesson before and after that work. Practicing is an integral part of it, and it doesn't sound like this teacher has put any thought into that.
To say that there is an explicit subtext of "blame" is an understatement- whatever you personally label that sentiment as. It's quite shockingly unfair to make such a speculation about an unknown teacher, simply because he is going on a completely standard summer teaching holiday (which is essentially all we can gather for definite from the OP's description). He hasn't even had the chance either to give or not give a summer plan and you're saying it sounds like he hasn't put any thought in- based on no more direct knowledge than the fact he is taking a holiday!!! That is spectacularly unfair and the assumption is based on totally inadequate information to justify it. Even if is so, assigning information on how and what to practise from week to week and through a six week period are totally different things. If anything, the better a teacher is at having showed students how to work week by week, the LESS he should need to talk them through some kind of pointless six week plan.
I appreciate that you are a teacher yourself, but what kind of things are you seriously expecting from a piano teacher? Precisely what are you claiming that a teacher has a responsibility to do- to plan out six weeks of unsupervised work? It's totally different to academic learning. A language teacher can simply assign a list of vocabulary and say to learn segments week by week without supervision. Music teaching does not function that way. If you've already worked at the student with their repertoire, you should need little more than to tell them to keep up with the principles that you have already showed them how to work at. If you're giving them brand new things, then either you have enormous trust in their talent or you've been outright reckless to leave them with what is simply self-teaching themself those things. That is, it's not reckless to be taking the holiday but reckless to be naive enough to think that a student can singlehandedly follow a useful six week programme without some feedback to keep it on a useful track- rather than a path to disaster. More often than not, such a plan will result in things being learned badly, in a way that builds deeply ingrained bad habits. All you can realistically do is ask them to stick to the path you were on in the last lesson.
That is the difference between piano and regular academic learning. The schedule must constantly change week by week according to needs that are particular to the moment for that student- or it is literally worthless. You can't plan ahead with a schedule that tells the student when they will urgently need to improve the quality of their thumb under technique, or in which week they need to remember the difference between forte and piano or in which week they need to stop forgetting F sharps. Without the feedback that makes weekly advice useful, a long term schedule is often worse than useless. A good teacher should instill the broad principles that students need. At the point of going on holiday, there is nothing useful that can be done other than a reminder that the student should keep up their work in the vein that it has already been shown to them in previous weeks.
The reality of the world is not ideal, but we can choose between worthless six week plans or we can accept both that teachers take holidays and that there's relatively little information they can give to make those six weeks optimally useful- other than that which they should be gradually instilling week by week. If the student can't be trusted to keep up what has been taught week by week, a detailed plan will make zero different to them. That's why it's probably a good idea to keep lessons going with another teacher, if the student is keen to keep going forwards.