As has been stated before. reasons include:
Many of which can be countered, if you actually know how Southern rolling stock works...! Not wishing to go round in circles, but seeing as we already are...
Less potential for delays as you only need a driver for the train to run, not 2 members of staff.
But to get 12 sets of bodyside cameras working some days is enough of an issue, then you've got all the problems with delays caused by things which a conductor can deal with (disruptive passengers, passcoms etc.) on a long train, very quickly, or at the very least in around half the time as a driver who also has to tell the signaller they're going to do it, shut down the cab, and then actually walk down to do it. I would be happy to agree that delays starting from origin stations will probably be marginally less, but Southern services already wait for drivers very regularly so waiting for crew is hardly going to go away. What I would argue is that delays due to technical or passenger-related problems en-route are likely to be significantly increased, and as a result, delays are more likely to be accrued at more minor stations with fewer lines and platforms to work round a problem, unlike the more major stations at which you would typically wait for a conductor, which usually (not always) have better facilities to loop trains awaiting crew.
Less delays waiting for the guard to open doors whilst issuing tickets.
Conductors only release doors on a handful of Southern trains and, on those where they do, it is considered imperative that revenue does not take precedence over door control. Thus it is much, much rarer for door opening to be delayed by this, in comparison with other networks.
Less delays whilst closing doors due to guard being stopped by someone on the platform asking a random question not even related the that train.
It is rare for customer service duties to delay dispatch - any which cause a distraction are to be politely ignored, something which is drummed into you from about day 1 or 2 of your training as a conductor...
Less influence over the railways from the RMT
Picking and choosing can end up happening a lot here. GTR and many other companies are perfectly happy to allow the RMT to deal with - and influence - many aspects of the railway, such as checking diagrams for validity. It seems to save the TOCs some effort on occasions, which I am sure they like. I'm not saying it's necessarily the right way of doing things but that point, in and of itself, may not always be seen as a benefit by the TOCs, let alone the RMT. It depends a lot on which policies or operational reasons it relates to!
Indeed GTR/the DfT were perfectly happy to negotiate a position where the RMT could carry out collective bargaining and representation arrangements for OBS staff, proving that some influence was always going to be permitted if they'd allowed a second person to be optional on board a train. I'm actually not sure what the position is with OBS collective bargaining and union representation now, but I should imagine it is somewhat more negative for the RMT than GTR/DfT would have been willing to improve on.
Lower running costs to operators (less staff to pay, less uniforms, smaller staff facilities needed etc)
There really won't be much if any change to things like staff facilities in the short or medium term if conductors are changed to OBSs, and not even if they were all made redundant. Mainly on the basis of historic reasons, there's a massive variation in staff facilities on the Southern network, and you will find that not a lot about this can actually be changed very quickly, in a lot of cases. At best it is a fringe benefit.
If you get rid of permanently-appointed railway staff then you will very often need to spend money for redundancy or severance pay, as well as spending money on people calculating it, and if you don't get rid of them but keep them in some sort of vaguely comparable job, actual pay costs and certainly the infrastructure to manage them will probably not differ that hugely.
As for uniform, in the case of GTR it's now been supplied in full to all current staff who need it, and therefore is now on an ad-hoc renewal scheme, so you're only looking at supplying full kit for new entrants; other than that, the design, supply infrastructure (such as it is, ho ho), much of the procurement, etc. are all done. So you're just looking at costs on an as-and-when basis. It can be calculated, I'm sure, but the actual savings may be minimal on the face of the whole TOC operations budget.
Extra 4 seats could be provided as no need for guard "office" where one is provided
You don't have conductors' offices on most Southern trains (they were even ripped out on the ex-170s). Only on the now-very-rare 442s, and even that's just a glorified luggage compartment really. Next...
I agree there are pros to guards but you only asked why no guards would help. There certainly are benefits...whether they outweigh the drawbacks is another matter and retaining guards in the OBS role does negate most of the "benefits" above, except the top three.
As you can see "no guards" (and, indeed, "no OBSs") provides a surprisingly small benefit, probably outweighed by negatives which are yet to emerge anyway. And we've already discussed what happens if there's another "Kentish Town", a major accident, PTI incident...
