These values come directly from the core rules (PHB 159). A skilled laborer makes 10x the earnings of an unskilled one. A highly-skilled laborer - a caster - makes 5-25x the earnings of a skilled one. Seeing as those numbers can be used in a simple way to put a reasonable (at least so far as emulating rl prices is concerned) value on slaves, it seems reasonable and good for consistency to go with them.
The only edition of D&D that really put thought behind its economics was 3e, when the difference between "skilled" and "unskilled" was several levels of the expert class and a significantly higher bonus.
It doesn't work as well in 5e where a "skilled worker" might just have proficiency, which is a 10% greater chance for success.
Even if there were more "worker" NPCs that had expertise, it would be a limited net benefit and likely not warrant the 10x increase in price. (Excluding the few rare tasks that *require* proficiency in a set of tools to even attempt.)
Regardless, skilled labourers are specialists. They do one job extremely well and charge high because they're not going to be doing it as often. That doesn't work as well for slaves, who are more general purpose. You don't get a bunch of specialists slaves because you're not going to need that slave every day (with the possible exception of a scribe or similar assistant).
Paying ten times the price for a slave you're mostly going to use a tenth as often a regular slave is foolish. You just hire an actual artisan for that task.
Arguably though, a skilled worked charges 10x as much because they can. Because capitalism. And, again, because they have lifestyle costs and might only find work every 2-5 days. A slave specialist doesn't have that same value, lifestyle costs, and the like. Their value is determined by the slave market rather than worker.
For a specialist being used every day (again, like a valet or chef) you would certainly pay more, but not necessarily *that* much more. After all, it's cheaper to just buy a youth at a tenth the price and train them for the role than buy the specialist. As per the PHB that will cost 250 gp (plus lifestyle, for another 25 gp) plus the cost of the slave. That's only 425 gp. It wouldn't take long for an established merchant to realise if they could sell that slave for only 1000 gp and make a tidy profit (or pay for two more slaves). But, again, this is assuming you paid full price for that slave. If you had people go out and capture & enslave people, the initial cost is 0 gp. While you'd need to occasionally hire slavers (2 gp/day for maybe 10 dudes), the initial cost might be just over 300 gp. So 400-500 gp nets you a decent profit.
5 unskilled slaves will eat 5 times as much as 1 skilled slave, and can't actually do the kind of tasks you need a skilled slave for.
Yes, those five unskilled slaves do need food. Likely less than 1sp a day (since you have your own house and such, this would likely be poor rather than wretched). The difference between the 5 unskilled slaves and 1 skilled slave is 750 gp, or 150 gp each. So you could feed those five slaves for 1500 days - or four years - for the money it would cost to upgrade to that one skilled slave.
However, to do all the odd tasks skilled tasks you might require skilled labour for, you'd need a dozen skilled slaves. The blacksmith, the woodcarver, the jewelsmith, the alchemist, etc.
Again, it's better to just go to a freeman blacksmith for the one day you need a horseshoe than buy a slave.
Also, I'm very much against the idea that if we can't fix everything we should fix nothing. I know you didn't say that - I just wanted to get it in before it came up.
