Why does a single pole tandem breaker allow connecting the switch handles?
The question isn't whether the breakers are able to accept a connecting pin.  The question is whether the manufacturer makes a UL-listed handle tie for those pins.   I would bet they do not.  

There might be a reason to handle-tie the inner breakers of two adjacent duplex breakers; i.e. In an A1 A2 B1 B2 arrangement, tying A2 to B1.  That would be for the normal uses of handle-ties, e.g. Multi-wire branch circuits and 240V-only loads. 

Also keep in mind, handle ties do not assure common trip; multi-pole breakers have an internal mechanism which does that.  (Which also means a multi-pole breaker is much more than two singles bolted together).  The purpose of handle ties is common maintenance shutoff, needed for 240V loads (which can have each leg separately fused), MWBCs (so you don't get nailed by the other leg), and 2 circuits on 1 yoke (ditto).