It depends. Cordless house phones can have as much functionality as mobiles nowadays, and work just the same (except they must be near the base). But the cost is an issue. AFAIK, there are no home phone tarrifs in the UK with inclusive or free texts. I have a mobile phone which has free unlimited texts, so why bother with a house phone. TBH I only have a landline for broadband cos a cant get cable.
When you get a text enabled phone, the first time you send a text BT converts your line so it no longer rings you and reads out the message, since they know you have a text enabled phone.
(Info based in UK)