I agree that designing an objectively reliable online voting system is very difficult. But at the same time I think that in principle it can be done. However, in my opinion the current unavailability of such a reliable system is not the largest issue with online voting.

Instead, it is its potential for giving the people with power more ability to control and enforce the voting behavior of the people over which they have some kind of influence.

For example, a boss can offer a bonus to employees who would verifiably (e.g. under supervision) cast an online vote according to the "company's recommendation". Or a landlord can say that the rent will be raised next month unless the tenant votes under the landlord's supervision and according to the landlord's preferences.

Such practices probably exist today as well. But the difference is that in the physical voting system, even the people who are being pressured to vote in a certain way are in the end required to be alone and behind a privacy screen while casting their vote. So, even if they have been forced to promise to vote in a certain way, they eventually have the freedom to vote as they like without having to fear that their actual voting behavior will be revealed.

That freedom originates from the requirement to cast a vote in private. Availability of online voting removes such a requirement.

Yes, that would help in theory. But in practice it would only change the way how the people inducing the pressure would verify that the votes have in fact been cast according to their preferences.

For instance, if voting multiple times is allowed and only the last vote counts, they would require the people to vote during the last 10 minutes of the polling period and afterwards they would withhold their ID card with the signing capability from them until the polling is closed.

If there are multiple private keys to choose from, they would require people to at first prove which one is usable for this particular election by checking it with the issuing authority. The owner must have been given this information in some verifiable form at some time, so the demand will simply extend to include that information as well.

How are all of your points different from mail voting?

The difference is small in theory.

But in practice, the availability of postal voting is limited. For instance, in my country you can only vote via mail in country-wide elections that do not have the second round. The reason is that it would be impractical to print the ballots for the second round and send them out all around the world in the time between the rounds, which is typically 2 weeks. Also, the destination at which you can receive the ballots must be abroad. There is no support for in-country postal voting. As a result, the potential for larger-scale influence-based misuse is significantly reduced.