...but spamming it every single time its available is just abuse of the system...
No, it's not abuse. Abuse would be using a system for a purpose it was not designed for, (with the easiest example being using chat to flame people. That's abusing the chat system.) and putting up the Surrender vote at any available opportunity - while in some cases may be annoying - is not abuse.
Punishment Ex: Chat bans or some other kind of punishment
A chat restriction (not a chat ban, mind you, they're different things, and chat bans aren't used) would be an improper punishment for hypothetical Surrender Vote abuse. Let's come up with a hypothetical scenario.
You're playing a match. It's a losing match, you know it, your team knows it, your neighbor's dog knows it, it's an L. You try to Surrender, but for whatever reason, two people vote no. You've said nothing throughout the entire match, and you don't intend to say anything now. You've communicated entirely through pings (bravo on that purely hypothetical feat, by the way), so you just quietly wait until the next opportunity. Surely to god in 3~ minutes they'll see the match is lost, right?
You start another Surrender vote. Green. Red. Green. Red. Vote fails. So you just quietly continue playing until the next opportunity.
The enemy team has broken all but one of your Nexus turrets, and you only barely got through that last teamfight. You try one last time to get that Surrender vote through, because you're down to one turret, and the enemy still has their Inhibitor turrets up. Red. Green. Green. Red. Vote fails. The match drags on for two more minutes, and ends in your defeat.
CONGRATULATIONS! You've now been Chat Restricted despite not using the chat at all.
You're greeted to a reform card devoid of chat logs and the warning that further punishments will be harsher.
D'you see how bad of an idea it is to try and use chat-related punishments for hypothetical offenses that do not involve the chat?