Garuda doesn't "save" you 5 ticks a minute.

It saves you roughly 1.8 GCDs a minute.

Its not like if you don't have garuda you simply won't have dots for 15 seconds.

It is that if you do have garuda you won't have to apply 45 seconds worth of DoTs. Which is roughly equivalent to 1.8 GCDs.

Since our weakest attack is ruin it saves you a whopping 144 potency or so.

Even if your math is correct garuda's damage contribution isn't nearly as high as you think it is.