Question: Is it really necessary to train your arms directly for good gains in muscle growth on that area?
The long answer to this question is, "it depends". Of course, there are so many variables we have to analyse and this issue has been beaten up to death already, so I'll do my best to simplify it.
First off, a disclaimer / prerequisite for this article: I've written a lot of arm articles in my time. I'm an advocate of direct training of the muscles of the arms with isolation movements, but it's dependent on the context of your situation.
Here's the short answer: No, direct arm training is not necessary at all. I haven't done two consecutive sessions of bicep curls of tricep work in over a year now, and my arms have shown no signs of atrophying, yet it's arguable whether they could've benefited at all during that time from additional work on them. They certainly haven't been to the negligence of my training performance though, and I'd venture to say most athletes would agree with me. Many of the most experienced strength trainees I know personally do not do any direct arm training such as various forms of curls or tricep extentions and their arm development is absolutely fine. In fact, it's impressive, to say the least.
So you don't have to train your arms directly to elicit gains in muscle mass, that's true. Most elite level lifters will agree with you. The average person should be stimulating arm growth a lot with the main compound movements they should be adhering to on a weekly basis and trying to progress at any way: weighted pull-ups / chin-ups, barbell rows, deadlifts, bench pressing, military press, dips, etc. All of these movements will provide more of a stimulus than most direct arm training, and I'll say this with confidence. A clear example would be to take all the lifters in your gym who strenuously perform these lifts to a high level and are strong, compared to the amount of guys you see investing too little time in them but performing a ton of arm work. Case closed.
However, there is another perspective to consider: will additional assistance work / hyertrophy specific stuff for your arms get them to grow to a worthwhile investment level? You have to decide what level of investment you're willing to put in, but the short answer is yes, additional work may undoubtedly help a lot of us and has worked well already for several million individuals, most probably.
Individuals who have poor genetics for their arms, need to improve strength and physical allure in these area's will benefit from additional arm training. Individuals who are also taking performance / physique enhancing drugs and AAS will also be able to have enhanced gains with additional arm work due to various subfactors that can promote growth that otherwise wouldn't be plausible to the extent it is.
As usual, it's a case of weighing up whether that constitutes the time or effort you desire given you can get perfectly good results off not training them at all. The choice is up to you.