Question: As far as I am aware,

1. HDMI 2.1 does support 12-bit 4K 60fps, Also it doesn't use TMDS, rather FRL. Sends upto 48Gbps
2. GPUs can do calculation in fp32 and from some reference, I think that it can send 16bpc (48-bit per pixel deep color) (Assuming that it is a high end Quadro GPU) (fp16 had the capability to send 12bpc 36-bit deep color, right?)

But there are monitors that don't support more than 10bpc 30-bit depth deep color

Why is that? Why do displays have limited bit-depth?

Can you give me some idea about the science behind this? Why does it cost more to produce higher bit-depth monitors?

Isn't it like, RGB pixels on the displays are emitting photons? Then how do different displays differ in terms of emitting photons?

Answer: 
The short answer is, cost. Higher bit-depths require more bandwidth at every point in the digital signal chain, from rendering unit, DRAM, link, all the way to the DACs that drive the panel.

Technology being what it is, as pipeline costs have come down, deeper color standards have been introduced, so panels have evolved along with the rest of the display ecosystem to offer both higher resolution and increased color depth. To enable this, HDMI 2.1 supports 8K and 48 bits per pixel now.

Looking further up the pipeline, cameras commonly support 12 bits, with 14 coming available (RAW modes). Editing systems already use 16 bits per component internally and quantize back down at the end when the work is finalized.

I should also mention the various HDR coding schemes that seek to improve display dynamic range in a more bit-efficient way than just adding more color bits.
1. Yes, true, but it also goes better than 12-bpc 4K 60Hz. It supports anything that goes up to 48 Gbps, and beyond that if DSC compression is used, the compressed stream is 48 Gbps so there is even more uncompressed bandwidth.
2. Certainly sounds possible. Many devices should support 16 bpc Deep Color just as easily as 12 or 10 bpc.

And yes, there are displays that support 12bpc. In fact if a HDMI display device supports 10bpc link, it must support 12bpc link too. Whether it actually uses those bits to drive the panel is something we cannot know. Note that the panel native depth may be less that what is possible by using dithering, so it is certainly possible to show images that equal 12 bpc with only a 10bpc panel, so that should count as a 12bpc display.

10 bits with HDR is slightly above the curve where eye can discern the quantization levels, but 12 bits with HDR is below the curve where eye cannot see a difference between quantization levels any more. If you have a 10-bit HDR capable panel and can make a display with adjustable backlight, preferably several separately dimmable areas, and work out some signal processing magic to get HDR image quality equaling to 11 bits with dithering and backlight control, there is no real visible improvement the human eyes can see.