while there are many considerations for whether technology should be used in a particular sport, perhaps a case can be made on how much decisions can affect the outcome. If a bad refereeing or umpiring decision has a greater chance of affecting the outcome, then surely that would be an argument for technology being used.
Football (soccer), I think, is the sport most amenable to the use of technology to assist referees. The scores are low and decisions can have a great impact on the outcome of the game. For a long time, the game in Australia was considered by a joke because of problems such as diving - a strategy that stemmed from how important getting awarded a penalty can be. Feigning can get another player sent off, as well as disrupting the flow of play. At times, the stakes are just so high that cheating or mistakes by the referee can have such a profound effect on the outcome that if there's the capacity to reduce that then surely it's for the good of the game to do so.
It's not saying that the technology needs to be perfect, but to ignore that technology can assist in the face of mistakes by referees having such profound outcomes is not an ideal solution, for fans, teams, or referees. It's not for the good of the game.