Actually, that's not true. Try pronouncing piano without putting that y in the middle. It sounds really weird and it's actually quite hard to say. PEE a no. You wind up with this weird break between the e sound and the a. PEE ya no is how that word is pronounced. And, as far as "going" is concerned, that's not where you put the break when you say that word. Try putting the break after the "o". It doesn't work.
Of course, there's the rule in English that you cannot place two vowel sounds together, which is why we add that additional sound in between. On a side note, having learned a language where you actually can put two vowel sounds together (Japanese does this all the time) it's really, REALLY hard for a second language learner to hear them.
Sorry, but you are a little off base here. From your other posts, it sounds like you have extrapolated a rule out of a useful if exaggerated demonstration for language-learners. However, there are fourteen phonotactic constraints (about as close to "rules" as it gets in linguistics) in English, and a requirement that every syllable have a consonantal onset is not one.
"PEE ya no" is certainly not how the word is pronounced. Most obviously, the stress is put on the second syllable. It is possible that it occurs on the first in some dialects [southern US?], but I believe that every national standard puts it on the second. I have no difficulty pronouncing it without a "y" sound, and placing the "n" in the onset of the final syllable either lengthens the "a" or gives the "n" a geminated sound, which
is against the "rules" in English. I pronounce it, with my broadcast-standard "American" (i.e., Iowa) accent, "pee AN o-oo", or, in IPA /pi'æn.oʊ/.
With "going," I put the break after the /ʊ/, whether it is suffixed with "-ing" or not. (Okay, I
can put it after the /o/, but it sounds like I'm putting on a foreign accent, because English loves its diphthongs.) The only native speakers I have heard put a /w/ in "going" even semi-regularly are Minnesotans, but then they also sometimes manage to fit one into "don't." Again allowing that a "w" sound may sometimes occur in rapid speech and in some dialects, I don't think that you will find one recorded in any national standard. If what you are saying were correct, there would be no appreciable difference between, "Go in the house," and "Go win the house." Granted, it is a distinction that is likely to give non-native speakers fits, but it is there.
In class I always use the following sentence: I am going to a party. How do you say that? "I yam go wing to wa par tee"
/aɪ æm 'goʊ.ɪŋ tu ə 'pɑɹ.ti/ (The American "u" is not actually in the cardinal position, and I could go drag up the specific symbol for it. . . . but let's not be pedantic.)
There are counter examples to your rule both contemporary--any vowel following a schwa, such as "mega apples" or "omega epsilon" or "tuba eater," seems unfit for a "y" or a "w" onset--and historical--"an apron" was once "a napron," but the sound migrated and the spelling changed.
The thing is, there is
some linking as you are describing, particularly with fricatives, approximants, and nasals, and I could see where this practice of interposing approximants between vowels could help non-native speakers to get from one to the next more fluidly and avoid unnatural pauses. Still, that doesn't make it a rule any more than, for example, "'did you' is always elided into 'didjou.'" I think you will find a large number of native speakers do not speak the way you have described.
The point being we typically (sorry, should have used that word the first time) do not begin syllables with a vowel e ve nif the wor dit self does be gin wi tha vowel. 
