I will copy here an answer that I have given more times to people asking how to learn kanji. As per the question "do I really need to?". No you don't, like you don't need to study Japanese. But the question is another one. If you find this 心電図 and you have never studied it before what are you gonna do? If you are lucky and know the meaning of those kanji you can easily get to know what that word means: heart+electrical+design, you can get to electrocardiogram. But if you do not know the meaning of each kanji? Or if the kanji is not so immediate? If you knew the reading of the kanji you could get to shindenzu and from there look it up in a dictionary...otherwise you will have to buy a kanji dictionary and trust me, looking up 3 kanji in those dictionaries takes much longer than looking up a hiragana written word.
Anyway, this is the answer I was talking about...
<<I think this will be different from person to person and also different people will give you different answers.
I personally use this site
Nihongo o Narau - Downloads and make my own flash cards with the help of 4 different dictionaries. So far I have learnt ON and KUN reading of 130 kanji, plus I know several other kanji that I meet doing exercises my tutor sends me.
Many people think that learning kanji is a monster, but it is really not like that. Many ON readings are recurring and mutual to many kanji. Out of those 130 I have found so many ON readings that are just せい、しょう or ちゅう or しょう...
Most of them are not that bad coz they do not have many readings and you will learn with time that many times a change in reading is just a minor change to adjust the sound of the kanji to meet different linking (according to what the next word starts with). Some kanji will be a real pain in the rear end suck as 生、上、下 and others for the many readings and others such as 付、立、当 and others for the many meanings they can assume. However as I said many kanji don't have that many readings, many have just 1 ON and 1 KUN or maybe 2 ON and 2 KUN.
The only thing I suggest if you go for learning readings, don't learn just a sound, but when you use the flashcards learn the different meanings per each reading. Learning a reading is good to look up in the dictionary compound words you have never met, but if you also learn the meanings you cut in half the use of dictionary. Of course learning all readings/meanings by heart is impossible and you will always miss some during your study, but it won't be that bad.
Last thing, I suggest you don't just learn the kanji sound, but the possibility of kana you can have following it. For example 足 would be easy to learn ソク、あし、た...but would it be enough? For soku and ashi yes coz they are nouns, but for ta it wouldn't coz it is the root of a verb. So when you study it, it would be better when repeating them to say ソク、あし、た（る）、た（りる）、た（す）。 I started with 20 flashcards and added 10 every time I felt ready and everyday at my lunchtime (at work) I repeat all 130 with all "complete" readings and meanings...
Done this way you will see it takes some time to learn kanji, but in my opinion it is a deep knowledge. A better understanding of a knaji than just studying a kanji with the reading and meaning of the occasion you will meet in 1 phrase.
But as I said this is a very personal choice. We all have different ways of learning.>>
You do whatever you prefer...oh and BTW, who said the kanji are only 1945???