For PC gaming they are far from mandatory. Those happen to be games with a lot of loading, and you seem particularly bothered by the loading. However, titles keep streaming more assets, lowering the amount of loading that is done and a SSD does not even help much in many games.
I love SSDs, but gaming is actually the last thing I would recommend it for. You need to compromise, there are few people in this thread that would not recommend a SSD, but at low budgets you have to make cuts. When you are gaming you constantly know the different between a high or low framerate or high and low settings, and with the SSD you only can know a difference at loading screens.
And you'd have a much lower capacity, with games getting bigger that is really not something you want.