The state-owned telcos were privatized in 90-ties, because the state is a bad owner, by ...state owned telcos from the west (Deutsche Telecom, Telefonica, etc). Of course, the first thing they tried was to move the obsolete equipment from their home countries to Eastern Europe for the price of a new one and for the money to get the new equipment in their home countries.
That didn't work out, because new competitors appeared, that built FTTH/Tripple Play networks from the scratch, with very low red tape at the time. That made the old DSL equipment not competetive in the cities (some even wanted to charge based on data transferred via DSLAM, making the flat-rate FTTH even better deal), so the ILECs had to do something with it - which meant to build their own FTTH network. DSLAMs were relegated to country side.
That's how Eastern Europe got fast and cheap fixed-line Internet in their cities. In the country, it is still mixed bag, better bet is LTE & 3G.
Eastern European countries mostly have great internet (especially landline, probably above average for mobile). I always assumed it must be because they came later to the party and went directly for modern technologies. As opposed to Germany who had telephone lines all over and then decided to get the most out of them because rebuilding with fiber would cost the companies too much.