Is it usual for finished PhD students to send out physical copies of their thesis to unknown persons?
This is not uncommon in the country where I did my PhD (the Netherlands). There you have to print a reasonably large amount of hardcopies anyway, typically people get around 200-300 copies in my field. It is not uncommon to send some copies to researchers that you genuinely believe may be interested in the work, usually people that you have been in contact with before, or are in contact with your advisor.

The cost of the thesis printing and mailing is generally reimbursed by the university (of course, all within reasonable limits). In countries where printing the thesis is not so common, I can imagine that the practice of mailing around copies is not common.