The only possible practical advantage of providing westbound Melbourne Metro Tunnel access for South Yarra passengers is travel to Domain, a journey of one stop. The 58 (nee 8) tram can cover these trips adequately, as it does now. (I'm ambivalent about the re-routing via Toorak Road West, but, from the point of view of this argument, it will make the journey a bit quicker.) For example, if you live in Caroline Street it is far quicker to walk down to Toorak Road, catch the tram a few stops to St Kilda Road (and the southern end of Domain) then walk or catch another tram to your destination than it would be to walk all the way to South Yarra, catch a train one stop to Domain, then walk or catch a tram down St Kilda Road. The situation won't change for travel to the CBD. You will still be able to catch a Sandringham line train direct to Flinders Street via one stop at Richmond, versus to CBD South via one-stop at Domain, or a Frankston line train direct to Melbourne Central via two stops at Richmond and Parliament, versus to CBD North via two stops at Domain and CBD South.
Paradoxically the passengers disadvantaged by no interchange at South Yarra, compared to existing arrangements, are those travelling from South Yarra or the Sandringham line to stations east of Caulfield on the Dandenong line. It introduces an extra interchange. If travelling from South Yarra you need to change at Caulfield, versus direct at the moment ,and if travelling from the Sandringham line you need to change at South Yarra and Caulfield, versus only changing at South Yarra. This could be minimised by scheduling Sandringham trains to arrive at South Yarra 2 mins (or whatever the average time for an interchange is) before a Frankston-bound train arrives and scheduling the Frankston train to arrive at Caulfield 2 mins before a Dandenong-bound train arrives and vice versa, at least in off-peak hours. Given the relatively few passengers involved, I think this is wildly optimistic and won't happen.
Extra peak hour capacity from South Yarra to the CBD can be provided by providing extra services on the Sandringham line, as suggested by Tony Morton of the Public Transport Users Association in The Age this week, or extending services from Flinders Street to terminate at South Yarra, as suggested above. If you accept that capacity on the rest of the Sandringham line is adequate, running extra services on this line is effectively running empty trains from South Yarra to Sandringham and back. If extra capacity is required south of South Yarra then this might be the preferable option, provided the trains weren't full by the time they arrived at South Yarra. The cost could be reduced by terminating some services at Elsternwick, if better crossovers, better signalling and, perhaps, a third platform were installed, or at Brighton Beach. The extending services from Flinders Street option provides direct access to North Melbourne and the line from which the services originated from, eg Williamstown. Either one of these options would be relatively cheap.