There may be a way to hack the default transclusion method but this would then apply to various core template functions and break them.
I think it would be unwise
Surely there will be cases where you do not want this default?
However if the problem is “So that I do not have to remember to apply my template all my future transclusions” there are other ways to simplify this.
For example in the editor toolbar there is a button to wrap some text in {{some}} you could make one to wrap the text in `{{some||my-template}}’
There are other methods available including
using macros <<my-template "some">> that does the same thing.
have the transclusion more than one deep.
To address existing transclusions you may be able to build a batch process to do this, however you must not apply this to other core and plugin transclusions.
In this kind of activity it is good to have the relink plugin as a helper.
The idea would be to redefine the transclude widget using a custom widget and then within the widget to re-issue the transclusion using the genesis widget with a default value applied to the template parameter. See the visible transclusion example for the general approach:
These changes could be applied locally by packaging them as a custom widget:
<$$set-default-transclusion-template template="foobar">
{{Boo}} is now treated as if it was {{Boo||foobar}}
</$$set-default-transclusion-template>