Hello Cyprus
Welcome to the SBB Community!
You can surely use the SBB Mobile App without the half fare card. If you still have the app installed, simply make sure the option is no longer activated when purchasing a ticket. Check that by clicking the pen icon displayed next to your name above the list ticket offers. See here:
https://community.sbb.ch/d/26418-how-can-i-save-the-info-of-swiss-half-fare-card
The system will automatically reload the offers without half fare.
And yes, it would be an issue; passengers travelling with a ½ fare ticket without the ½ card do pay per passenger a surcharge of CHF 70 plus the other half of the ticket.
Whether it makes sense to purchase the Swiss Half Fare Card? If you plan to spend CHF 240 on tickets per person you are break even. Depending on your travel plans and the number of mountain excurses you are planning in, the card is worth its money, in particular when you travel in addition with children which can benefit from free trips thanks to the complimentary Swiss Family Card.
Kind regards,
Roland