The reading of the title of the question reads as a poll asking for examples. If this is what is desired, then it is off topic because polling itself implies that there are multiple correct answers that may be at odds with each other.

While P.SE does stretch it a bit, from help - don't ask:

You should only ask practical, answerable questions based on actual problems that you face.

Asking for "Are there any real-world practical problems where only the best (exact) solution algorithm or program will do (but not the good-enough solution)?" - it is unclear what the actual problem that is faced is. This is where the unclear closure likely comes from.

Additionally, the last paragraph of the question:

I think that we live in a world where it is required from programming solutions to practical purposes to be good enough. In rare cases really very very good but still not the best ones. Isn't it? If it's not can you provide an example of such solved or unsolved problem of practical interest?

This sounds like a call for a discussion. Discussions don't work well in the Q&A format. We welcome such in chat, but as questions they just don't work.

The key for this to be reopened would be to address these issues in the question - don't poll for examples, make it clear what the problem that needs to be solved is, and don't try to have a discussion about the topic.

The reading of the title of the question reads as a poll asking for examples. If this is what is desired, then it is off topic because polling itself implies that there are multiple correct answers that may be at odds with each other.

While P.SE does stretch it a bit, from help - don't ask:

You should only ask practical, answerable questions based on actual problems that you face.

Asking for "Are there any real-world practical problems where only the best (exact) solution algorithm or program will do (but not the good-enough solution)?" - it is unclear what the actual problem that is faced is. This is where the unclear closure likely comes from.

Additionally, the last paragraph of the question:

I think that we live in a world where it is required from programming solutions to practical purposes to be good enough. In rare cases really very very good but still not the best ones. Isn't it? If it's not can you provide an example of such solved or unsolved problem of practical interest?

This sounds like a call for a discussion. Discussions don't work well in the Q&A format. We welcome such in chat, but as questions they just don't work.

The key for this to be reopened would be to address these issues in the question - don't poll for examples, make it clear what the problem that needs to be solved is, and don't try to have a discussion about the topic.