One of the core ideas behind politeness and etiquette is that you assume no malice (or willful negligence) when there is nothing to indicate malice or willful negligence.
There are perfectly reasonable explanations why the person in question was late, many of which are no justifiable cause to blame them for being late.
The fact that you have a meeting with these people suggests that meeting people is what they do for a living. Not every meeting's duration can be accurately estimated beforehand, many of these meetings are susceptible to the actual topic of discussion, and can vary in length based on the client/patient's situation.
As an example, my doctor allows for online appointments to be made in 15 minute intervals. However, that doesn't mean that my doctor abruptly ends the consultation after exactly 15 minutes.
If an appointment ends up taking longer, then so be it. The alternative (kicking out a patient) is much worse than a minor delay, and these delays should average out in the long term (some appointments take less than the scheduled 15 minutes).
Saying nothing would forgive their lateness: but I refuse to, as their lateness is not pardonable, disrupts scheduling, and mentally distresses me.
- It is pardonable, especially if you don't know the reason for them being late yet!
- It does indeed disrupt scheduling, but keep in mind that this affects the person's scheduling too! If you make an appointment with someone, and it gets delayed, all participants have to suffer the delay.
- Mental distress is not a fair argument here. You're exaggerating the issue. Unless your appointment was with a mental health physician about your oversensitivity to human error (I concede that this comes across as a bit tongue-in-cheek, but it's the only acceptable scenario I can think of)
Schedules can be delayed, they are not intentional nor malicious, and you need to learn how to deal with unintended accidents, or at the very least respond to them in an appropriate measure.
- I'd first utter one of the following (interrogative) statements
The fact that you label such a question as interrogative suggests that there is an underlying hostility to your question.
That underlying hostility, when detected or inferred by the other person, would completely negate any polite phrasing you use.
One of 1.1-1.3 would be followed by a second (declarative) statement
Now you move on to declarative statements. Why?
Why are you the one making a statement, when you're in fact unsure why this person was late? You're being presumptuous.
The lateness worried me not least because it will disrupt my scheduling and the wait wasted my time.
- "Not least because" is unnecessarily hostile.
- A delayed appointment inherently leads to a disrupted schedule. That's the literal definition of a delay. You're stating the obvious, which comes across as complaining for the sake of complaining.
- If you have a valid complaint, use a concrete justification. Don't say "it wastes my time", say "I have another appointment soon". Without a concrete complaint, the validity of your complaint is easily questioned.
In order to remain polite, you should never assume that the lateness was unwarranted, malicious or caused by willfull (or reckless) negligence.
If your intention is to reprimand this person for their lateness, any attempt at being polite has inherently failed before you've even said anything. It is the nature of your interaction that is offensive, regardless of how you phrase it.
There are better ways to approach this, my preferred approach would be to casually ask if the person is having a busy day.
Note the stress on the casual nature of your request. You're asking a question out of curiosity, not because you are owed an explanation or are trying to reprimand this person for being late.
- Do not assume malice or incompetence. Be understanding that things sometimes don't work out the way you plan them. This applies to every living creature.
- Do not try to reprimand this person for their lateness. You're not their mother, nor are you their boss. Before you act, consider what would happen if you end up running late for your next appointment with this person, for a completely understandable reason that is not your fault.
- Although it would be polite for this person to explain why they were late, you are not owed an explanation. If you imply (or outright state) that you are owed an explanation, then you come across as feeling entitled, which is nowhere near polite.
- If you have a valid issue with the meeting being delayed, use a concrete explanation. Don't just try to argue the general point of how valuable your time is.
- Any hostility from your end, whether implicit or explicit, will dramatically affect the interactions with this person in the future.
- You're allowed to ask nicely why they were late. If you wish to avoid coming across as intrusive, simply ask if they are having a busy day. This way, you come across as interested in this person's wellbeing (i.e. their current stress level), rather than trying to berate them for not being on time.