This isn't directed at the OP but those who practise the concept in general.
I wouldn't ask visitors to remove their shoes at the door because I think the object of being a host is to be welcoming and put someone at their ease (to a point!)
When a host asks their visitor (whether it be friends, family, acquaintances, handymen etc), whether they would mind removing their shoes and stands over their arched backs watching them unzipping, unbuckling and untying, there is a power play of kinds occuring; that may not be the host's intention but the discomfort and inconvenience is how it may make the visitor feel.
Once I've offered to take visitors' coats, I'd like them to sit down and make themselves comfortable -fast. It disrupts the flow of conviviality if the funniest thing that happened today is recounted to you via a muffled voice, three inches from the floor and you're watching the back of someone's head as they're telling you. If the visitors are older and they have to hold onto the back of a chair or side of a door frame to steady themselves when they remove footwear, it seems quite grand to suggest they do.
The inference is that the visitor may 'infect' the house or 'spoil' the carpet with their shoes.
Status quo must be maintained. To be frank, if the host is the one imposing rules, then perhaps it should be the host making the effort to discomfort his or herself rather than the visitor. They could cock a leg and allow the host to clean their soles with an anti-bac wipe then it would be seen as the host's indulgence.
At what point during this process does the host take the gift the visitor has usually brought with them? Before or after the instruction? "Oh right, thanks, stop! Don't step further, no, no, stop right there, yes by the door, if you wouldn't mind removing ..."?
I understand the debate about animal faeces being walked into the house or more likely in this era, TB/hepatitus bacteria from human spittle but past children's crawling age, it does seem bit neurotic much. The visitors could well have been sitting on a train/bus/pub seat in the same clothes they're now sitting on your sofa in or the last time their hands may have been washed may have been at dawn. If they walk around in their socks at home and also wear shoes on the same floor, then it's a pointless request. Where does it end? If the concern about bacteria is so profound then when not have wood floors that can be washed easily or a sheep dip at the entrance 
There are times, too, when you don't necessarily want you visitor to get too comfortable and asking them to remove shoes indicates an invitation to relaxation that isn't intended. I don't want that man with the clipboard, however nice, getting too cosy. I think I'd rather wonder what's on the underside of his shoe than witness the sight of a jaudiced toenail seeping through a clammy, threadbare sock.