As a long time Salesforce user, as well as developer, I can tell you that most users don't build reports to begin with. Reporting, in general, tends to be left for administrators and managers, and they should be able to remember to filter converted leads. Furthermore, most managers and administrators don't build reports every day; they build it once, save it, and probably never/rarely update it ever again. While reporting is arguably one of the most useful features in Salesforce, it's relatively rare to see people constructing new reports on a regular basis.
As for why it's the default mode, it is presumably because it's the fewest number of filters. There are exactly zero built-in reports that include any custom filters (which "Converted equals false" is). It's the same reason why opportunity reports don't filter on only open opportunities, even though that might be a reasonable default in some people's minds. While in your case, you tend to prefer to see only unconverted leads, this is only a convenience for you. It's perfectly natural to assume that other organizations might care only for converted leads, but there's no default for them, either ("Converted equals true").
You can't generally hide converted leads, as they're still right where you left them upon conversion. Some organizations prefer to delete them, but others prefer to preserve them for reporting purposes (ROI, lead source revenue, etc). While you might find it inconvenient, the truth is, that a neutral filter (both converted and not) is the only filter that makes sense from a neutral reporting perspective.