I'd rate Smart at over $20 million a year. He is earning significantly less than that ($12.5mil) - so yes, he deserves a raise.
Smart is a top 10 SG in the league. His impact as a defender, passer, ball-handler, outside shooter, driver, rebounder make him more valuable than guys who score the ball more than he does but lack his all-around game. That is why I rate Smart as a top 10 SG and worth over $20mil per year.
I'd go even further and argue that he's worth a max contract if he sustains his current offensive production throughout the season. I don't see why he shouldn't earn a max if he's a free agent next offseason, his combination of top tier non-big defense and valuable complementary offense (decent outside shooting on good volume, very good secondary playmaking on good ball security) makes him an All-Star who's no "worse" than the likes of Tobias Harris.
Smart is worth no where near a max contract. You just can't pay that for 11 ppg, 5 apg, 3 rpg, even if it comes with elite level defense. You start throwing that kind of money around for that and you end up crippling your team. Smart is in the Patrick Beverly, Avery Bradley, Tony Allen, etc. level of player. Very solid role player, but a role player none-the-less. Those guys are worth more than the MLE, but no where near the max. That is borne out historically. Even someone like Draymond Green has never made the max and Green is better than Smart (at least at his peak) in virtually every way.
Draymond Green took paycuts to stay at Golden State in order to win titles, he would've gotten multiple max contracts if he wasn't willing to sacrifice his earnings for winning. And Smart's better than those counting stats, he's not averaging very gaudy numbers due to his role on offense (4th option at best) on this team that has 4 really good players in front of him, he'd be averaging something like 14-15 PPG, 6-7 APG and 4-5 RPG per game in a larger role to go along with his top tier non-big defense.
Patrick Beverley, Avery Bradley and Tony Allen are nowhere near Smart's level on defense, Smart's versatility to check wings and even bigs at times makes his defensive value closer to elite defensive wings rather than his guard contemporaries. Add in Smart's newfound ability to actually initiate an offense this season with his playmaking, as well as his improved three point shooting and it's easy to see that Smart is closer to a smaller Draymond than those three players you've mentioned, which makes him a max level player (or at least near max level).
After 5 seasons, Smart had 1 1st Team All Defense. Beverly, for comparison, had a 2nd Team and a 1st Team. After 5 seasons, Beverly was basically a 10/4/3 type player though never had a TS% lower than 50.9% and was over 54.5% four times. Smart's TS% his first four seasons was under 49.2%, only in year five did he finally elevate it up to a respectable level of 56.8%. Beverly was also a full time starter (after his rookie year) and not a back-up. After his 8th season when Beverly was 30, the best he could do was 3 years, 40 million, which annually more than doubled any previous seasons salary in his career.
Draymond signed his second contract after his 3rd year as a restricted free agent for 5 years, 82 million. That was a good 30 million under the salary cap. No team came anywhere close to offering Green that kind of money and frankly, even coming off the title I'm not so sure the Warriors would have matched a 4 year, 90ish million dollar offer (which was around the 4 year max). During that 3rd season he finished 2nd in DPOY, was 1st team All Defense and averaged basically 12/8/4 along with 1.6 steals and 1.3 blocks. Plus the Warriors won the title, and yet he came no where close to a max contract offer. Smart has never come close to a season that good and the best Draymond could do was 5 years, 82 million.
Smart is worth no where close to a max contract. He just isn't. He might get slightly more than the 4 year, 52 million he signed for on the open market, but it wouldn't be much more than that as players like him just don't move the needle in that way. They are great role players that any team would be lucky to have, but they don't merit huge contracts.