Several thoughts here:
1. The Restored Church of God (to whose web site the original post linked) is an offshoot of Herbert Armstrong's Worldwide Church of God, and is a majorly wacky cult probably worse than the JWs.
2. There is not one instance in the Bible where Jesus Himself is said to have gone from house to house. If this were such an indispensable feature of Christian ministry, one would think it would be explicitly stated that the Lord Himself had done so. Telling His disciples to go to people's homes is not the same thing as commanding them to engage in door-to-door evangelism - of course they would go to people's homes to instruct them in an age where there was no TV, radio, Internet, printed Bibles or literature or other means of mass communication. Going to people’s homes does not equate to knocking randomly at the doors of strangers.
3. The Greek term translated "from house to house" in Acts 20:20 can also be translated "in private homes," and the context indicates that it is much better translated that way there. Paul was not talking about some sort of door to door evangelism program in those verses, he was talking about how he instructed the ELDERS of the Ephesian church. Again, it's not surprising that he would go to their private homes in order to instruct them. The way JWs try to use that verse, we would have to understand that Paul went up and down the streets of Ephesus, randomly knocking on doors until he found an elder of the church, then would go in and instruct him. Doesn't make nearly as much sense.
4. The only verse in the NT that could possibly be used in support of door to door type evangelism by any early Christians would be Acts 5:42, but the same Greek phrase could as easily also be translated there as "in private homes," and would make just as much sense. In the absence of other evidence for early Christian door to door preaching, we cannot assert this text as sole proof, since its meaning in this matter is not conclusive. We would have to be reading our idea of door to door evangelism into the verse rather than drawing it out. Even if the early Christians did use this method of evangelizing, it would not necessarily mean that such a method is required for Christians today, since there are much more effective methods of reaching large numbers of people that don't carry the negative social implications associated today with making uninvited visits to the homes of strangers. There is no command anywhere in Scripture to preach specifically from house to house; the concept is imposed on the text by JWs, not drawn from the text.
5. As far as the effectiveness of such door to door ministry, it is actually very ineffective. If you divide their hours spent in "field service" by the number of baptisms for (for example) the year 2011 (as reported in their Yearbook), you find that 5,451 hours had to be spent in their ministry for every new baptism that occurred, and that's not taking into consideration that the majority of those baptisms were probably of young people who had been raised as JWs. That doesn't sound like a very effective method of spreading the word to me. A cynical mind (such as mine) might conclude that the purpose of the door-knocking work for JWs is to keep them so busy that they don't have time to ask questions, rather than to effectively spread their message.
Not that there is anything wrong with knocking on doors if it's what one feels comfortable to do and one wants to evangelize in that fashion (though I think there are also some very good arguments against it in this day and age), but it is hardly a required activity for Christians, as the WTS teaches.