I know this may sound weird but I’m not actually memorizing these kanji at all. I only recognize what they look like. The reason I say this is because when I read a kanji in different fonts or handwritten I have a hard time discerning. Also if you were to ask me which radicals the kanji compose of I can’t even tell you. Rather than seeing the individual radicals my brain just lump the kanji into an image and that’s how I recognize a kanji when I see it.
That’s mostly good though. You don’t want to have to break down every kanji all the time to read anything. The main things breaking down kanji is useful for is writing, differentiating similar looking kanji, and sometimes to help with meaning/reading (since kanji generally have phonetic and semantic components). For more about phonetic components, see [Userscript] Keisei 形声 Semantic-Phonetic Composition.
For that I’d recommend using Jitai (字体): The font randomizer that fits. This script will change fronts during reviews at random. You can install your own fonts and add them to the script if you want even more variation.
That’s why I use Flaming Durtles and Jitai, and downloaded a bunch of fonts to mix it up. I’ll also echo seanblue’s recommendation of Keisei, which is the biggest thing that keeps me from just doing everything on Flaming Durtles.
I think that’s pretty normal and not that different from when we learned our own written language. You weren’t reading cursive at first, you were reading block capital letters and then lower case, and then cursive, and then yada yada. It’s a process of getting more and more used to it.
I agree with what other people are saying about this generally being a ‘good’ thing and that it’s natural, after getting used to a writing system, to see things in blocks without needing to break them down. That’s how Chinese speakers (like myself) sometimes make mistakes when rushing through a text because we see a particular character and substitute a similar-looking one for it in our heads, only to realise it makes no sense later. The general shape is sometimes all we’re looking for.
However, I’m just going to stick my head out there and say that knowing how to identify radicals, or at least meaningful, familiar parts (that you might not find a in a dictionary radical list), is going to be necessary if you want to be able to identify kanji in various forms. Sure, there are stylised kanji that even native speakers will find hard to decipher, and that’s normal, but the reason native speakers are able to break those down is that they know what makes up the kanji. That’s also why, provided you know some of the ‘conversion rules’, even deciphering certain archaic characters is possible, like those in a goshuin stamp mark from a temple. It’s a useful skill, so I’d recommend you maintain an awareness of components and radicals, even if you certainly don’t need to keep breaking kanji down if you can recognise them. I think the scripts provided by @seanblue will be helpful for practice.
*since many common kanji have them. I wish they were more widespread, but semanto-phonetic compound kanji aren’t the only sorts of compounds, and you occasionally get ridiculous compounds that are super complex while sounding nothing like their components. For example, 専 and 恵 both contain the same ‘meaning’ component, even in their traditional forms, but their on’yomi are nothing alike: せん vs けい. However, a simplified form of 専 is used as a phonetic component in words like 転 and 伝 though.
Anyway, I’m just quibbling. It might be confusing to hunt for a phonetic component in a compound kanji only to find none, but the knowledge that this is one of the major ways compound kanji are formed is very helpful indeed.