yes, what he said. Although in Winnie the Pooh, the non-rhotic 'r' was not to distinguish 'ther' from 'the' but to emphasise the definite article. The contrast is between Pooh without the article and 'THE Pooh.' In some mystical, never explained way, somehow Winnie THE Pooh is a boy's name, even though Winnie is a girl's name.
Besides, 'aizit' would be pronounced like eye-zit, not the same sound at all. The diphthong 'ai' by itself normally communicates the sound found in 'aisle' and is not the same sound as the ai in air, hair, chair, fair, etc (i.e. æ), whether or not you pronounce the 'r.'
"And, why "airzit garn" and not "rarirarirt rgrarn"?" Because that's not where you put intrusive/non-rhotic 'r's - see the thread called 'pigeon towed'
pigeon towed for previous discussion about non-rhotic spelling and pronunciation.
