I think anime's popularity in the west has gone in peaks and troughs since roughly the late 80's, the most recent peak being the early 00's explosion during which the industry probably reached too far. The following "crash" combined with the subsequent global financial crisis kinda fucked up both the anime industry and Japan's video game industry. As a result, both have decided to double down on the very most hardcore fans with an increased focus on loli and fanservice anime, which is off-putting to pretty much anyone else. Loli and fanservice were always a thing in anime, at least since the 80's, but I feel like it's become a bigger part of the anime industry over the last few years, and it's repelling more westerners.
That industry waning also severely lessened the amount of broadcast anime which I think has given it less exposure. A whole generation of anime fans started out on Toonami when it exposed them to the likes of DBZ and Gundam. There's nothing putting anime like that on mainstream TV these days. Toonami's late Saturday night block, Funimation's streaming site, other localization producer sites, and Crunchyroll are great if you're already into anime, but it's not gonna cross the vision of someone new to it. Hulu has a ton of anime as well, but I don't know how often those shows might show up on the front page. Same goes for Netflix.
Provocative, mature anime like many of the greats from the 90's and 00's (Bebop, Ghost in the Shell, Trigun, etc.) are still being produced today, but they are probably harder to find. They also get less attention than the fanservice stuff these days. I can definitely admit I watch a lot less anime now than I did 10 years ago. When I look at the chart for the latest season of anime it's pretty much just a shitload of high school drama shows, many filled with fanservice, and maybe one other type of show I might be interested in. Right now I'm only watching the Buu Saga in Dragon Ball Kai, Space Dandy Season 2 on my DVR, and I'm going to check out what Zankyou no Terror is like. Luckily, over the last couple years a lot of the classics from the previous 20 years are finally being released on Blu-Ray in the west: The Ghibli movies, Tenchi, Cowboy Bebop, DBZ, Ghost in the Shell, Lain, basically the stuff that got current fans into anime.
I think the most major thing people forget about anime is how diverse it is. People often ask Yahtzee of Zero Punctuation what he thinks of anime (expecting he has views similar to Giant Bomb) and he always says in reply that you can't really like or hate *all* anime because it isn't really a genre, it's a medium.