Looking at the photo, I would myself move the derailer claw hanger forward about 1/8", since it looks like there is yet plenty of grip surface on the dropouts and because the chain appears so tight on the big/big so as to possibly cause slow ("tight") shifting off of the largest cog.

There are many reasons why never to use the small/small combination (I said many), but why does anyone advise against using the big/big? It's one of the most-useful gears in the entire range, given that it allows the rider to avoid ceding momentum with a front downshift when cresting a hill.

Note that a sufficiently-long chain is needed especially with older single-sprung-pivoted derailers like the OP's, otherwise the chain gap may become sharply larger as the largest cog is engaged. Too much gap requires the derailer to overshift the largest cog in order to make the shift, which risks putting the chain over into the spokes!
Additionally, largest-cog-size limits of the particular derailer must be respected, especially when these are bigger than published figures from the manufacturer.

But, with any sort of modern chain (why use anything else!), there should be absolutely no other concerns about crossing the chain from big-to-big, given that these older bikes typically have longer stays and narrower cog stacks. Only if the bike is so poorly set up so as to have the crankset outward from where the chainrings are centered within the freewheel's width (which is common enough) ...but even with an outwardly-positioned crankset I still use the big-big even for sustained climbing. It's not like the chain or cogs are going to wear out prematurely, that just doesn't happen(!), but using the small/small combo increases and/or contrates loading and/or wear greatly on the entire load path (through the frame and all), as well as chipping up the chainstay paint right away.

Admittedly, there are bikes out there with front derailers not optimized for using the entire range of cogs while in the big ring, but careful adjustments, narrow chain (and subtle, carefully-considered cage tweaks where needed) can easily gain full use of the freewheel's range without ever having to "trim" the front derailer's shifter.

End of rant, but I use the entire spread of even 8, 9 and 10-speed cassettes in the big ring, even on bikes with short 40.5cm chainstays.