Ubuntu 18.04 LTS with Intel HD 630 and nvidia RTX2060 fails to load the Intel driver

Question

I have a system with two graphics cards. The integrated one (Intel 630) and an nVidia. Monitor is connected to Intel HDMI port. My aim is to have the PC display(Ubuntu desktop etc..) on Intel and dedicate the nVidia card for CUDA operatations.

nVidia works fine.
Ubuntu desktop is getting displayed but its performance is poor. Video playback flickers and the CPU gets immediately hogged. Its apparent that the driver for intel card fails to be loaded thus the video processing goes to CPU.

On system details, I see:
Graphics: llvmpipe (LLVM 9.0, 256 bits) - which confirms the above suspicion.

Hardware seems to be correctly recognized:

$ lspci | egrep 'VGA|3D'
00:02.0 VGA compatible controller: Intel Corporation HD Graphics 630 (rev 04)
01:00.0 VGA compatible controller: NVIDIA Corporation Device 1f08 (rev a1)

$ sudo lshw -c video

  *-display                 
       description: VGA compatible controller
       product: NVIDIA Corporation
       vendor: NVIDIA Corporation
       physical id: 0
       bus info: pci@0000:01:00.0
       version: a1
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress vga_controller bus_master cap_list rom
       configuration: driver=nvidia latency=0
       resources: irq:130 memory:de000000-deffffff memory:c0000000-cfffffff memory:d0000000-d1ffffff ioport:e000(size=128) memory:df000000-df07ffff

  *-display
       description: VGA compatible controller
       product: HD Graphics 630
       vendor: Intel Corporation
       physical id: 2
       bus info: pci@0000:00:02.0
       version: 04
       width: 64 bits
       clock: 33MHz
       capabilities: pciexpress msi pm vga_controller bus_master cap_list rom
       configuration: driver=i915 latency=0
       resources: irq:127 memory:dd000000-ddffffff memory:b0000000-bfffffff ioport:f000(size=64) memory:c0000-dffff

$ sudo prime-select intel
Info: the intel profile is already set

Everyone pretty much suggests that the Intel driver should be automatically installed by Ubuntu. Seems that this is not the case. Any help will be highly appreciated!