Is it safe and effective to have "glider pilot mentality" when landing single-engine fixed-wing aircraft?
Diamond aircraft are very low drag and do not have particularly effective flaps, so sideslipping is certainly an effective way to approach the problem. However there are considerations you need to be aware of:


A steeper approach can bring you down on top of another airplane on final approach. Maintaining a more common approach angle is safer as it is less likely to bring you into a potential collision, and keeps you on a path where other pilots are likely to see you
Steep sideslips are not particularly comfortable for passengers, the steep angle and different feel can be frightening
Having your engine idle for long periods can lead to ice buildup in your carburetor, even with the heat on. It also lets your engine cool down quite a bit. Keeping some revs on keeps things warm up front
A steep approach angle makes it harder to round out accurately
A mishandled sideslip can lead to a loss of control. If the ball is to one side and you get past the critical AoA you will be executing a snap roll at low altitude, which = bad


There's nothing wrong with using sideslip and keeping up with the technique - it's very useful if you catch a thermal on approach, are given a slam dunk approach, or need to get on the ground fast. For me it's not the best tool for normal approaches when you have alternatives, especially if you come in at a very steep approach angle. 

One technique I've heard of for approaches on Diamond single engine airplanes is to use a combination of both: a slight sideslip dirties up the airflow enough to create some useful drag, and power is used to maintain the approach angle. 

I can't think of a light airplane you can't sideslip, or any airplane you can't sideslip for that matter (perhaps the Mig 15). Sideslipping was used successfully in the Gimli Glider incident, and that was a 767! There are limitations which will be listed in the aircraft documentation, for instance you should not sideslip a C152 above 20 degrees of flap. If I'm flying a C150/152/170/172 I follow that rule.