'Then' is not a conjunction

I find that some students mistreat the word ‘then’ as a conjunction. So, they can mistakenly have the following sentence pattern.

'I overslept this morning, then I was late for work.'

Although ‘then’ and ‘so’ both have the meaning of ‘since that is the case’, they cannot be used in the same way. The former is an adverb while the latter is a conjunction. As a result, the above sentence can be written in the following either ways:

'I overslept this morning, so I was late for work.'
'I overslept this morning, and then I was late for work.'

Although in an informal style the word 'and' can be dropped, it holds for that with ellipsis. For example,

'David worked first, (and) then Susan (worked).