They rely on using software to display all the info... which is a possible attack vector ie. an attacker can get hacked versions of the software loaded onto your device(s) and display whatever they want... and trick you into confirming a transaction that sends all your funds to some unseen address etc.
This is why the newer wallets all tend to include screens... it makes it harder for this attack to succeed as the attacker would also need to compromise the device itself to display "bad data"... which is generally orders of magnitude more difficult than compromising software on a PC/tablet/phone