Chris' answer notwithstanding, there's an additional 'oddness' to that song...
You can think of the song as having two 'choruses' - one in the verse & another in the chorus itself.
I think I'd be inclined to call it a Refrain rather than a chorus, if viewed this way - it also echoes Chris' sentiment of it being a call & response song.
Oh the summer time is coming
And the trees are sweetly blooming
And the wild mountain thyme
Grows around the blooming heather
Will ye go, lassie, go
And we'll all go together
To pluck wild mountain thyme
All around the blooming heather
Will ye go, lassie go
Considered this way, you have a two-line verse leading the story, followed by a "warm-up" to the chorus, almost as though it's needed to teach the audience how the next bit goes.
Then you get the 'let's all join in' bit, with a simple opening line that everyone will soon pick up - "And we'll all go together"
Straight after that you get the repeated refrain, which they've now heard before & will find it easier to sing along to, if not the first time, then increasingly confidently with each refrain.
If you consider the first time any given audience ever heard this song, way way back before recording or even sheet music, you can imagine the singer guiding them over the first couple of verses - by the end they'd all be much more confident as each opportunity arose to join in.
That the 'call' of the verses changes through the song, yet the 'response' of the singalong refrain remains the same, gives the story-teller opportunity to further the tale, whilst still reminding the audience of the refrain to come.
Bear in mind this is not some po-faced 'tell the audience how miserable life is' song, it's a pure celebration of the coming summer, & an invitation with romantic intent; sung in the evening with perhaps a not inconsiderable amount of ale to lubricate the vocal chords. It's a sing-along crowd-pleaser, which is perhaps why it's survived the centuries so well.