Yes, cities should destory abandoned and foreclosed homes to prevent blight, crime, and sinking home prices. If a house has been abandoned, leaving it there to rot and drop neighboring house prices is just not fair. There should be a time limit on how long a house stays abandoned before the city can take over and destroy the home to free up the land.
I live near Detroit and the abandoned houses there attract so much crime and lower the real-estate value significantly. Some are historical and have big potential. Tearing down the majority of them would help decrease the crime and allow for the historical ones to gain value again while giving space for new homes.
The sight is such a common one that it's easy not to even think about it anymore: boarded up houses in various states of neglect dot the landscape of many major cities. These homes not only look unsightly, but they bring down the value of surrounding homes and provide a safe haven for criminal elements. They should be torn down.
In cities such as Detroit, there are so many abandoned homes that have historical value. These homes are diamonds in the rough and could be brought back to life by the right investors. It would be such a shame to destroy homes with beautiful original details and woodwork that is hiding under a layer of dust.
Cities should not destroy abandoned or foreclosed homes, that should fall on whatever entity is responsible for the home. For example, in a foreclosed home the bank that holds the title must take responsibility for the home. If they are unable to maintain it, they should sell it at auction. As for abandoned homes, if an owner can not be traced, and the city should likewise sell the home.
Houses don't exist for the good of the real-estate agent, the exist for the good of the families who will live in them. If banks have evicted families because they were not able to pay overpriced mortgages with usurious interest we need not protect their investment. The price of the houses will drop and those same families may be able to afford the now more reasonably priced homes.
Dilapidated and dangerous houses are a different story. If a building is structurally unsound the city ought to require the owner (the bank) either to fix it or to destroy it rather than letting it rot and leaving it accessible to criminals.