normally soft-combining isn't used in WIFI systems, because it violates stateless nature of the internet protocol stack.
I would argue that 802.11 is not a "stateless" protocol in the networking sense when infrastructure mode (most common use of 802.11) is employed. The 802.11 client must "negotiate a connection" to authenticate/associate to the infrastructure and the infrastructure maintains a "session" for the client until they disconnect (or time out in some manner).
Not sure if your professor misspoke, you misunderstood what your professor said, or you didn't communicate what your professor said correctly here. Either way I would disagree with this statement.
I was wondering whether the IEEE specification for WIFI allows for ARQ with soft-combining.
No, it doesn't as it currently stands. Soft combining (generally referred to as HARQ) is not really possible with 802.11 because it isn't workable in the 802.11 PHY as it stands, but HARQ has been discussed and considered for 802.11 a number of times.
While there was talk about including HARQ in 802.11ax, it was ultimately rejected. One of the concerns is that the advantages of HARQ may not provide any sort of benefit in the relatively high collision environment of 802.11. It would have also required too much work/too many changes to the PHY and there were other needs that were of higher priority.
There is again talk of including HARQ in 802.11be, and I would expect to see some studies published in the coming year or two to evaluate the effectiveness of HARQ for 802.11 traffic. Only time will tell if it will be included in the finished ammendment.
References for more reading where HARQ is mentioned in conjunction with 802.11:
- Minutes from the July 2018 IEEE EHT (802.11be) TIG meeting show a brief mention that HARQ was again forwarded as a feature to be included - Word Document
- Blog article that details some of the possible features that may be included with 802.11be (part of a series)
- Cornell University publication on 802.11be - PDF Document
- Old study on impact of HARQ on 802.11a showing negligible gain (not that it really applies to modern 802.11) - PDF Document