VBAT pin and external crystals in STM32F030R8T6
1) High-Speed clock

Typically, the tolerance on internal MCU oscillators is bad. It is very difficult for manufacturers to trim the internal RC network that generates the frequency to obtain something stable and accurate. In the MCU you mention, for example, the HSI is 8MHz +/-1%, which is very inaccurate for a time reference. USB, for example, which is made to be easily implementable and does not require very accurate timings, still requires +/-0.25% for full-speed communication. So, in this case, you need a crystal. A crystal typically has +/-50-100ppm tolerance (0.005%-0.01%).

From a consumption point of view, however, you'd better use the HSI than a crystal. The crystal requires an oscillator circuit that usually consumes more (at least for crystals in the 8MHz range).

And, yes, the prescaler allows to run the MCU at a lower frequency than the HSI or crystal. But this is available whatever the timing source is.

2) Low-Speed clock

If you look at page 60, you'll see the internal low speed oscillator (LSI) can be anywhere from 30KHz to 50KHz. So, it would accumulate up to 6 hours of error a day! And the 1% HSI clock, 15 minutes a day. So, if you need less than +-5 seconds per day of drift, you need a crystal. And if you do the math, you even need a 50ppm crystal (at least).

Otherwise, there would be no problem in dividing the LSI frequency by 40000 rather than 32768 to obtain a ~1 second timer. The hardware allows this.

3) VBAT

There is no VBAT pin, indeed. And this functionality is not provided by one of the VDD pin. It simply does not exist on this MCU. However, you could have some external circuitry to supply the whole chip with the battery when the normal supply is not available (e.g. with or-ing diodes), and put the MCU in standby mode (with LSE active) so you don't draw too much current on the battery. But it is less paractical indeed.