I heard a song named "因为爱所以爱"， literally it means "love because of love". Though logically true, is it not a tautology here? Do we really say phrases like the following ones in everyday Chinese?
You could interpret the title as "(we) love because (we wanted) love"
It is a kind of tautology to a lesser degree, as it is less redundant as oppose to phase like "I already say that again".
Also song title are often conceptual, where songs are usually for expressing intangibles afterall. Hence the examples you provided are not some phase you'll hear daily.
the saying of the same thing twice in different words, generally considered to be a fault of style (e.g., they arrived one after the other in succession )
'one after the other' and 'in succession' are the same thing in different words , so one of them is redundant.
"因为爱所以爱” or 为爱而爱 (to love because of love) follows a common phrase structure [因为 X 所以 Y] or simply [为 X 而 Y]
X is the reason; Y is the resulted action
In "因为貪心所以殺人" (Killing because of greed), 貪心 is the reason; 殺人 is the resulted action
In "因为恐惧所以屈服" (Yield because of fear), 恐惧 is the reason; 屈服 is the resulted action
In "因为爱所以爱” (Love because of love), 爱 is the reason; 爱 is the resulted action
Notice, when the reason is the same as the resulted action, it means you do something because you wanted to do something with no other reason.
Killing for Killing's sake (为殺人而殺人)= You kill because you wanted to kill (因为想殺人而殺人)
Love for love's sake (为爱而爱)= You love because you wanted to love (因为想爱而爱)
To make "因为爱所以爱” sound more nature, you can either not omit '想' and write "因为想爱所以爱” (I love because I wanted to love) or replace '因为' with '為了' and write "為了爱而爱" or simply "為爱而爱" (love for love's sake)
The main point of the title "因为爱所以爱” is "it doesn't need a reason to love"
Since neither 爱 is redundant in this sentence, it is not tautology, just a flawed sentence