I think there are a lot of variables that are important to answering that- mainly being what you want to do with him (ie, I remember you saying in your intro that you wanted to do dog sports with him) as well as his level or reactivity and the nature of it (ie, disruptive anxiety vs disruptive anxiety that may turn to aggression vs aggression/level of aggression), how willing you are to risk it becoming worse, and how much time you have/how dedicated you are willing to be on this issue.
I am a firm believer that reactivity is a problem in any dog, and that any aggressive dog can cause injury to another dog or human and can pose a threat, but realistically the nature of the aggression and the size of the dog have to come into play on this kind of decision, IMO. A human/stranger or dog aggressive great dane is a huge problem and needs professional attention at any level of aggression; still a problem if it's a very human aggressive chihuahua, less of a problem if it's a dog aggressive chihuahua, IMO, because management will be easier for a small breed than a giant one and the chihuahua is less likely to be able to really harm most dogs.
He's a Springer Spaniel, correct? They are a medium sized dog able to do some damage for both humans and dogs, and big enough to kill a lot of smaller dog breeds if they are very aggressive. They also tend to lend themselves to nervous temperaments, IME, which can mean they get worse as they age without attention being paid to the issue.
If you really want to compete in dog sports, you will likely be paying someone to train you one-one-one for the sport and his issues of reactivity could be put in there as well.
If you are going to spend the next year reading every book about this you can and willing to do some trial-and-error and he isn't that bad right now (ie, not dangerous, just annoying), I think maybe you could see what it feels like to try making a plan of it yourself for a few months and seeing how he does, but I also think that there is a level of anxiety or aggression where a professional makes the situation safer.
I think part of the reason why there are so many reactive dogs in the world is because a lot of people will get a dog and not notice warning signs when the dog is younger that it may need extra attention in being OK with strange people or dogs, or maybe might have issues with other dogs growing up, etc. For example, a young puppy displaying a lot of nervous behavior or calming signals in the presence of another dog that is perfectly calm and ignoring it, or a young puppy growling at a stranger. It's a lot easier to start working on these sorts of problems before they get a chance to escalate, especially when it's not a small dog. If it's people aggression I would continue working with a trainer no matter what, if he's having problems with other dogs... I have had a dog that had sever dog aggression and we never got her help- granted she was a 15lb Boston Terrier, but we pretty much just were careful on walks and didn't let her off leash or bring her places where we knew there would be other dogs. It was kind of a bummer and I sometimes think I didn't help her live life to the fullest because she was still super afraid (it was definitely fear based aggression) until she was eventually pts at 9 (for an unrelated issue), but it was OK.
How bad is it? Is he just a little anxious or is he seeming like he may eventually attack a dog or person? Did you make any plan with any of these trainers for long-term management? What are your hopes with this- are you trying to get him to be a competitive performance dog, just be able to compete with him a little in dog sports, be comfortable in his environment all the time, just not be dangerous even if he is a little anxious, manage as needed for the rest of his life...?