Is there a way to have an OKR that has no end (time period)

I do understand. I did make mention that the specific ones I am talking about are in fact more of a purpose statement. We do have OKR like you mentioned though (most of them are key results though). For us, it is just nice to be able to align them to these purpose statements because it links the actual measurable to the purpose of the role who owns the set of objectives. However, Viva goals doesn't seem to let me not select or have some sort of open end date. So, I may just use a different tool to manage the different purpose statements and keep Viva goals to the more traditional OKR.

I do have a question about your example though, because it points out an issue I keep run into regularly.

Objective: Reduce customer wait times by 50% by the end of quarter.
Key Result: Reduce customer wait times by 50%.

I often run into the objective and the Key Result basically being the same thing. Especially, in Viva Goals where something like Reduce Customer wait times by 50% seems to be what you would make the key result. So what i have been doing is something like the following:

Objective: Improve guest experience. (something like that)
Key Result: Average wait time reduced to 30min (Q1-Q2)
Key Rusult: Everage wait time reduced to 20 min (Q3-Q4)
Key Result: Customer check average increased to $XXX (Q1-Q4)
etc.

the objective does have the end in this case. and it completion is based on the key results.

Anyway, I often run into the issue of the objective basically sounding like one of the key results if i get to concise with it.