It is a good idea if that's what you want to do. It could be a bad idea if you don't want to drive more three hours.
I don't deal in "should" - that's your choice. It certainly can be done, and if you want to, you can do it.
You will, in additional to the additional charge your rental company wants (although that's a surprise to me) you absolutely need to affix a Swiss toll vignette to the windscreen. That sticker is valid for a whole calendar year and costs CHF 40 (around 40 €) and there is no short term version. Don't try to skip the Vignette - fines are high. You can get it a fuel stations as you approach the border or at the border if it is a staffed entry (most are). Slow down for tunnels - most have a speed limit of 80 kph. That's for safety after various issues in the past. The tunnels themselves are beautiful and so well built. The speed limit is strictly enforced. Don't be surprised to see highway exits and entrances inside the tunnels.
I love driving in Switzerland and do it whenever I get the chance.