LDO vs. DC2DC for 3.3V to 1.05V Converting
Note: the load for this circuit is VL805 ‧ VL806 - Super Speed USB 3.0
Host Controller, which unfortunately I can't share it's datasheet due
to confidentiality concerns.

The main consideration is power dissipation and I have used a figure of 300 mA for the load current. Less or more, the process is the same. It's a guess of course!
The RT9186A has (at best) a thermal resistance of 105°C/watt. So, if the average output current is (say) 300 mA, the power dissipation will be: -
$$\text{300 mA}\cdot\left[\text{3.3 volts - 1.05 volts}\right] = \text{675 mW}$$
This will raise the junction above the case by 71°C for the VDFN-8L device and 108°C for the MSOP device.
If the local ambient temperature is (say) 25°C the junction of the VDFN-8L device will rise to 96°C and, for the MSOP, it will rise to 133°C. Then after a short while, due to localized heating, the local temperature may increase by another 20°C. This means the junction could rise to 116°C or 153°C (device dependent).
The limit is 150°C so, in this simplistic method, you might be concerned about the MSOP part.
Nothing more can really be added without knowledge of the load and that is being kept secret due to confidentiality. You will, I'm sure need to provide significant copper around the part to help with power dissipation but, that's for you to decide.
However, one trick you could use is a dropper resistor feeding the regulator's power supply input. Given that the proposed regulator can work from an input supply voltage of 2.5 volts, the dropper resistor could &quot;lose&quot; (say) 0.6 volts at full current (say 300 mA) and the regulator's power dissipation would reduce from 675 mW to around 495 mW. The resistor would of course dissipate the extra but, it might be a preferable solution.