if using a good quality road bike frame with not so beefy carbon fork i would be alright with 28mm tires.
i did ride a Scapin EOS 7 that had a woundup fork. it could not fit more than 28mm tires. i was alright with a 18-19mm inner width front rim.
last road-ish bike i used was a chopped up CX that had oversized tubing with 35mm/37mm front/rear. the rims were about 19mm inner width.
this type of frame.
now i roll on a 29er MTB with only the front brake and 1.6"/2" front/rear. rims are 21mm inner width. i miss the first bike more than i miss the second.