Well well well, this can of slices is getting bigger and bigger with no end to it.
If you want daily level data which is stored blobs you need slices, that is millions of records if you time frame and number objects so determine. It does not make any difference in that respect if the slices are custom defined or OOTB.
I suggested custom slice for 2011, because I got the impression you do not want data from 2011 to the current date, but some part of that on the early end.
Careful now when you say TSV. If you have what is normally called TSV attributes they create new slice definitions and records. Even though (assignment) actuals are time varying they are not normally referred as TSV (where I come from)
There are a number of views and portlets which can display eg project actuals, ETC and other in timescaled views. They use also slices, but system slices and they definitely do not go back to 2011.
If you do not want slices and want data that goes back to 2011 you need something like third party "Time Slicer", but the community code of ethics prevents promoting commercial third party products.
Please educate me
"I am talking about the restrictions on out of the box range that can be defined"
I still do not know what you are referring to. Have not yet come across restrictions for the OOTB slices either.