Tend to agree. But if you work in a team, there will be someone who just loves implicits and overloading and you won't be able to change his mind. Strong code style policies help, but they are really rare in real processes.
Your team can make a decision as a group to not allow defining operators in the team's codebase. As you mentioned you can then enforce that with scalastyle (set FieldNamesChecker and MethodNamesChecker regexes to ^[a-z][A-Za-z0-9_]*$). Is that not enough to handle the one person who loves overloading?
That time when my boss started using "implicit" on everything. We were even using a new "Functional Relational Mapping" framework from Lightbend/Typesafe called Slick which was a mess.
Most libraries — SBT is one example — have shifted away from the use of excessive overloading.