I have 3 dogs, all adult large breeds. The elder of my 2 GSD isn't neutered but that's purely because he's epileptic and the risks of surgery are too great.
My Lab came to me as an adult rescue dog and was neutered, as any reputable rescue should ensure before rehoming. My younger GSD was also a rescue dog but a pup and so I had him neutered when he was nearly 2. My vets advice was to wait until he was cocking his leg - he's now 5 and if I'd have carried on waiting he'd still be unneutered!
Neutering reduces or eliminates the risk of some serious illnesses and of dog/dog aggression and mounting, the latter of which is not only embarrassing if he does it to the vicar but also dangerous if he does it to another male who will take offence to it as many do. However, it's not just that. For me just as important is reducing the risk of my dog escaping to find a mate and getting hurt, killed or picked up by a dog warden or unscrupulous person, never to be seen again and eliminating the possibility of him adding to the already huge unwanted dog population in this country.
As a rescuer I get to learn of daily a huge number of healthy, perfectly lovely dogs who are in pounds, desperate for rescue to come forward and save their lives. There are far fewer rescue spaces than there are unwanted dogs and many of those pound dogs don't make it but leave the pound in black plastic bin liners, dead.
I fight like buggery to find what few rescue places there are for such dogs and, like all responsible rescuers, fight equally to beg people to neuter their own dogs and not to add to that number.
I'm aware of the argument against neutering above but for the very, very vast majority of dogs the op is a simple one with no lasting ill effects and much to gain. I would argue back that if that was not the case rescues up and down the country would not insist on neutering and neither would vets. It can be counter argued of course that there's profit in it for the vets but there certainly isn't financial gain in it for rescue, quite the opposite so why would they insist upon it were it not for the overall good of the individual dog and for dogkind? Likewise there's no profit in the RSPCA charity hospitals, the PDSA or Dogs Trust neutering but nonetheless they advocate it strongly and insist upon it for the dogs which they rehome.