removing offsides would encourage teams to play very conservatively/defensively. You even see this happen in Golden Goal situations (which is when teams are in overtime and the next goal ends the game). More often than not, both teams end up playing very conservatively, waiting for the other team to push up too far so they can easily counter and score. Golden Goal was an idea that was introduced in an attempt to finish games sooner, but the result is that those games often end up going to shoot outs because neither team wants to be aggressive.