As far as specialization, there's a school of military thought that says role specialization is bad, or at least suboptimal, and that interchangeability is good. If your tank driver, your infantryman, and your pilot are all held to equal physical standards and given equal training, then you can have your pilots shoot people or your tank driver fly a gunship if the need arises. Normally that's not entirely feasible because of different body types, limits on how long you can spend training someone, etc. but those limitations don't apply here. (There's an example of this in action in Shatterpoint, where Mace Windu calls in a clone force of mobile infantry that also ends up operating a major spaceport and acting as pilots. Normally these would be three very different groups of soldiers.)
As far as safeguards, there's no reason to assume they would be in trouble if a particular clone didn't work out. They mention some modifications are made of the template (but not Boba in particular; they mention this specifically). Presumably the Kaminoans would follow normal industrial procedures such as making prototypes to ensure the viability of their final genome, and keeping adequate backups of all the work they were doing in case of any problems. (They also might not have, of course, but that would be a problem entirely separate from using just the one template.) This is also a reason to use just one template: more templates means more time and money spent on preproduction in the form of tinkering with genomes and trying out prototypes, and it means more complications with quality assurance later on.
Regarding environmental constraints, it's not likely that they're going to see a major improvement without finding templates of a totally different species. It comes down to whether the clones are going to be expected to fight in hostile environments often enough, and whether they're hampered enough by environment suits or other protective gear, that it's worth the inevitable cost of adding more templates.
Regarding vulnerabilities, I have to assume some of the modification done to the template was to remove any clear genetic defects that would hamper them. That doesn't mean they'll turn out perfect in every case, of course, but any non-genetic problems would presumably crop up at the same rate whether there was 1 or 10 or 1000 templates.
Finally, it might be worth pointing out that this was supposed to be a secret. Each person who gets made into a template is a person who now knows about (or can deduce) the existence of the Grand Army.
So in short: there are distinct advantages to using one template in terms of cost, production time, interchangeability of clone roles, and secrecy, and the disadvantages you gave could largely be worked around with some genetics and ordinary mass-production procedures.