Cannot you ask for a ticket to the beginning of the zone ?

No.

Page K1.5 in the NFM
(http://www.atoc.org/retail/_download...4_Common_K.pdf) says:
"Excess fare tickets must never be issued to a Travelcard Zone or
combination of Zones. They may only be issued from a Boundary Zone to
destinations, and at fares shown, in Section K3."

Yes you can ask for a ticket to the beginning of the zone.

That bit of the National Fares Manual describes that tickets _can_ be
issued to the _beginning_ (in practise, the outer boundary) of a zone
(as the OP asked) - for use in conjunction with a ticket valid within
it. The term used is "boundary", so the destination will be printed as
"Boundary Zone 6". The rule quoted above distinguishes between this and
issuing an excess fare to be used anywhere within a zone, as with LUL
tickets for example.

Don't count on the fare being cheaper than that to the first station
inside the boundary, though. That would be far too simple.

To give an example of this in practise (although the "other way
around"):

Earlier this week I travelled from Acton Central (in zone 2) to Watford
North (outside the zones). I held a Travelcard season for zones 2-4. I
therefore purchased a single ticket from "Boundary Zone 4" to Watford
North, and was able to purchase this my origin station. This works out
cheaper than a single for Acton Central-Watford North, and does not
"duplicate ticket validity".