You can't paste transitions to multiple edit points, but you can apply transitions to multiple edit points. After you've specified your default transition duration (Preferences > General) and your default transition (right-click the transition you want in the Effects panel > Set Selected as Default Transition), select all the clips you want the transitions applied to, and then go to Sequence > Apply Default Transitions to Selection. This will apply both video and audio transitions, but if you make your selection while holding Alt/Opt, you can override clip linking so that you can apply only video transitions or only audio transitions. You can also select non-contiguous sections by using the Shift key, in concert with or without the Alt/Opt key.
Thanks Colin. You just added years to my life.
I can honestly say that's the first time I've had such a remark made in my direction! (Usually, it's the opposite )
Glad to help!