Why do we need to increase sampling frequency at the transmitter?
Three reasons to increasing the sampling rate further are

1) To relax the requirements of the post D/A conversion filtering for image rejection.

2) Increase signal SNR by spreading quantization noise for a fixed number of DAC bits across a wider frequency range.

3) Minimize passband droop in the D/A reconstruction.

Reason 1 is the most dominant one in my opinion. The complexity and cost of a low pass filter (either digital or analog, but in this case it is the analog filter) is driven by the width of the transition band. And the reason for filtering the images is usually spectral containment as limited by regulatory requirements (and given the value of spectrum this is a HUGE reason). Reason 2 is a solid consideration if your DAC is limited by the number of bits but has wider analog BW and sufficient Spurious-Free-Dynamic Range (SFDR) to allow for overssampling benefits. Reason 3 is of least impact but I mention it as it is indeed a benefit. To address reason 3 we can often optionally simply incorporate an inverse Sinc filter digitally to compensate for the passband droop from the D/A (and this can be quite simple- see how to make CIC compensation filter). 

Note interpolating DAC architectures do this for you- increase the sampling rate prior to conversion to simplify the analog anti-imaging filter requirements and give you more bits effectively since the same total quantization noise power is spread across a wider frequency range, some of which is then filtered out by the anti-imaging filter.

These graphic by Walt Kester of Analog Devices in their App Note MT-017 (https://www.analog.com/media/cn/training-seminars/tutorials/MT-017.pdf) shows this very well (Thanks Walt!):




To add, there is no benefit to the performance (sideband rejection) of the pulse shaping filter by increasing the sampling rate. The pulse shaping filters rejection is completely driven by how many symbols it spans. Two samples per symbol are all that is needed. Having more samples per symbol in pulse shaping does however simplify subsequent digital filtering if a post shaping interpolator is used- but this is exactly the same benefit described above for simplifying the analog anti-imaging filter, for the same reason.