Dealing with a engine failure when you know one is coming, like what will happen in training is a whole different animal than dealing with the sudden unexpected lurch to one side. I do not think most twin training does a very good job of preparing twin owners for real world emergencies.
Also my personal observation is most privately operated twins are flown by pilot who do not seem willing to do regular recurrent training and more importantly do not have the personal discipline to follow the important SOP's that this equipment needs to actually benefit from the second engine.
For example I teach (and do myself !) a run through the engine fail vital actions, including lightly touching the relevant controls (to build muscle memory) before every takeoff and have a predetermined no/go vs go point in the takeoff.
As for the question of doing your PPL on a twin.......well my thought is just because you can do something doesn't mean you should. This being a perfect example. The best way to learn the foundation handling skills is in a light low powered trainer, with simple systems allowing you to concentrate on looking out the windscreen, and which flies on the wing not on the engine(s).