The "new broom" has to make her mark and dress code is as good as any - it will be visible, but comparitively innocuous, unlike some new bosses who may seek to reduce the wage bill by 10%......
For a man working in administration of any sort I think a shirt and tie is literally a no-brainer as it does away with all discussion of what's right or acceptable etc. Many millions have worked with ease for hundreds of years without even thinking about it.
I witnessed the "dressing down" era, initially on Fridays, where some people rolled out of bed into the office, unshaven and unwashed. This for some quickly became the daily norm but it was too late to start disciplining folk..
"Public Facing" is a red herring - all workplaces are visited at times by customers or potential customers, whether external or internal and the old saying still stands, "first impressions count".
Untidy people inevitably leads to untidy workplaces - if you doubt me, find out where the IT people are in your workplace and pay them a visit.....they are the ones that started all this because they could - they had to be left in peace to practice their black arts, so geeks workplaces are just like geeks bedrooms...