It's important, imo, to know exactly what is happening when you are castrating a dog and thus greatly reducing the testosterone levels.
Testosterone has a number of influences but in a nutshell (ha!) it reduces the threshold to aggression and triggers sexual behaviours. This means that a dog is more likely to use aggression at a lower level of provocation than a neutered dog. Sexual behaviours are marking, roaming, mounting, territorial aggression etc.
However, it also increases confidence meaning the dog is less likely to be provoked in the first place. This not only counteracts the above but seems to go further in that a couple of more recent studies have strongly suggested neutered dogs are far more likely to display fear-aggression than intact males.
From a behavioural pov you have to look at the dog you have. Battendog is one who can be nervous sometimes and this is one of the reasons he still has his balls at 13 months old. If I had a dog who was mounting everything, or displaying territorial aggression I may consider neutering (alongside behavioural management techniques) instead.
From a health pov testosterone acts to prevent bones growing too long. An intact male is more likely to be shorter and stockier than one neutered while his bones were still growing. This elongation and additional growth can increase the chances of bones cancers which are more common in neutered than intact (especially when neutered young, in the first couple of years of life).
However, removing the testicles does remove the chance of testicular cancers. I think studies have shown neutered dogs are more likely to die from cancers whereas intact makes are more likely to die from infectious diseases and trauma (e.g. car accident). Presumably because intact males are more likely to engage in risky behaviours such as roaming.
Another reason Battendog is left intact is because he is a big springer - I'd like him to get all his growth well and truly done before messing with his hormones.
For me, I take the view that the testicles are there for all sorts of reasons and so, unless I have a very good reason to remove them, Battendog can keep hold of them. That said, the best any of us can do is read up on the latest science knowledge and make the best decision we can for the dog we have, in the environment we have them in.
fwiw I had no issues finding a walker and day care to take him. I am always wary of theft, though as his massively-obvious pink balls (tmi?) seem to me to be an advertisement to thieves.