Can't the digital signal be transmitted without converting to analog signal like how our voice is transmitted through the line?
By one definition of analogue and digital, all physcially transmitted signals are analogue (the analogue domain, continuous in time and amplitude, and that includes square waves because of course a real square wave is never a perfect constant amplitude). All signals in computer memory are digital (the digital domain, discrete in time and amplitude).
But the more common definition of analogue and digital signal are as follows: When someone says digital signal they mean an analogue signal in which digital data is encoded, and the receiver decodes the signal into a binary data packet. An analogue TV displays the received signal where the actual received voltages are used to control the brightness of the electron gun for each colour directly. This is what people usually mean by analogue. There's no ADC that samples the signal converting it into digital data points to be processed digitally and classified into bit sequences and packets of data, which can contain further error correcting. Similarly, the VGA interface is analogue because the voltage signal directly drives the electron gun in the analogue domain after manipulation only from analogue components that treat the signal as a voltage signal as opposed to a microcontroller that treats it as encoding binary data and samples it and places it into memory (digital domain) for processing. VGA was built for CRT monitors but became a standard, and LCD displays were made backwards compatible with it by containing an ADC – indeed people still calling it analogue becomes questionable in this case because the analogue voltage signal no longer directly drives the display, and given there's also a DAC on the transmitting end, it's just effectively a digital signal (digital data encoded in an analogue signal) now transmitting amplitude modulated amplitude samples, so you just have to remember that the VGA signal is still able to drive analogue displays directly, which is why it's still called analogue.
It's the same thing with a modem in a router. It converts the data in the digital domain (the router memory) to an analogue wave transmitted on the wire (waves can only be analogue). The diagrams that show digital between the PC and modem but analogue between the modems is misleading. Any physically separate device requires an analogue transmission (with digital data encoded in it), so it is analogue between modem and PC. Using the definition of digital signal in the previous paragraph however, the diagram should surely show digital between PC and modem, and digital between modem and modem, because they're both digital signals, but instead the diagram shows analogue between the two modems.
I think the reason for this is because it's assumed to not be a physically point to point link between 2 digital nodes (the 2 modems, that will interpret the signal digitally), but instead passes across analogue switches that treat it as a purely analogue signal, and apply analogue processing it it as if it were the analogue voice signals it was designed for. It could also be because it considers the PC, router, modem as the digital domain (they could all be the same device accessing the same memory) and the analogue transmission line is indeed analogue and transmits digitally encoded signals. It could also be that transmission via local serial cables (ethernet, rs232) between the devices tend to baseband transmissions that resemble square waves i.e. what people associate with a digital signal, whereas the transmission over the phone line is modulated up and looks like what people associated with an analogue wave.
To recap, I'd say that an analogue signal is one that is created by an analogue source (microphone) and the intended and standardised output device is an analogue one to be directly driven by the signal and it is able to do so, even though this signal of course can actually being digitally sampled at the receiver. An analogue signal is also a signal that is digitally generated using a DAC but the intended and standardised output device is an analogue one to be directly driven by the signal and it is able to do so, such as a VGA signal is intended for and is able to drive a CRT. If there is an ADC it does not change the fact that it is an analogue standard and therefore an analogue signal. A digital signal is one that is created in the analogue or digital domain and it is intended for a receiver that extracts digital information from it to memory. Of course the signal could power an LED or something, but that is not the intended receipt of the signal, and it does not change the fact that it is a digital signal, until you define your own separate standard driving an analogue LED and then it would be an analogue signal.