There's no hard and fast answer here. It's all about looking at management expense and the total cost (CAPEX and OPEX) of the computers involved and making a choice.
I don't have any Customers who have thin-client devices (to any great degree) and most of them have at least one PC dedicated per employee. (With the kind of businesses I work with there ends up being no cost savings "win" to going w/ thin clients once you factor in all the licensing expense, setup labor, etc.)
Most of my Customers have a desire for out-of-business hours remote access. Using their existing desktop PCs on desks as single-user Terminal Server computers is generally a good cost proposition in these circumstances. The PC is already setup to present the user's expected environment and, obviously, there's no Terminal Server to setup and license.
If the desktop PCs are being shared by multiple users (shift work, for example) the PC becomes unavailable as a single-user Terminal Server. In that case, something else must be done. That's where I'd start looking at a dedicated Terminal Server.
This isn't the case for most of my Customers, so I don't have dedicated Terminal Services machines (for the most part). If I did, I'd think long and hard about removing the desktop PCs and transitioning to thin clients anyway. I definitely wouldn't want to be in the situation of having both the expense of a desktop computer and a Terminal Server seat for the same user.