The problem of short trips with the consequences mentioned above is real for most of bikes, especially water cooled.
For a 1200 HD, instead, 10 mins are enough IMO: HD engines get hot after very few minutes.
The only problem could be in the exhausts, being them quite long thus better cooled (the stock ones: if you have a shorter one the problem is reduced).
Condensation with possible rust problem in mid term is behind the corner, but I'd see this mostly in cold outside air, not for summer.
One minute (no more) of engine idle before starting the trip should reduce this problem to almost zero also in winter.
Regarding the battery recharge, you just need a longer trip at weekends, and not necessarily every weekend, and everything is ok.
Ciao
Ugo