The purpose of Sentinels, for me, is the play style.
First some background. <old man yells at clouds> My first 50 back in the day was an Energy/Energy/Force blaster. I got there in the days of SOs. I mostly solo'd with the occasional help from a friend who ran a Dark/Regen scrapper. I got started on my blaster after they had nerfed range as a decent defense besides running away. All mobs' melee and ranged attacks were effectively identical damage wise. I solo'd almost the entirety of the AV arc, minus Infernal (?) with his insane regen and room of adds and one other which was an accidental team completion. By the time I hit 50 I had all but the last xp debt badge. I did all the things I was supposed to do. I kited*, I loved my snipe, I bailed when appropriate, and I ate inspirations like a starving man. I loved blasting, but I hated every minute of the fragility. Unfortunately, it was the ranged primary AT at the time. (With the same amount of effort and slotting, my Dark/Dark/Dark Def was a virtual god.)
Once I hit 50 and unlocked the HEATs, I rolled a PB and never looked back. I had squid when it was safe to blast, lobster when it wasn't safe to exist, and human form for everything else. Unfortunately, PBs needed a group to shine. Even with heavy SO slotting, human form had damage worse than defenders and defenses worse than a scrapper. (Sound familiar?) But I was willing to trade the poor damage for some defenses. If I can be forgiven the pun, I actually had a blast. Mild ranged + mild defense was my jam. Then later PBs got some major upgrades and much later IO sets were a thing to make them even better.
Fast forward to Homecoming. Sentinels. Everything I liked about PB with none of the micromanaging.
Ya see, in the last 20 years of gaming, TTRPGs included, I've found that I like characters that work out of the box. No special gear beyond the basics. I don't want to spend a stupid amount of gold or influence or whatever to be awesome. And I certainly don't want to grind to get there. (This especially applies to D&D where you can't rely on your GM to deliver the goods you need.) Blasters don't really work out of the box. Oh, they're okay. Stressfully dancing on a razors edge is always there. But you need to spend inf to get them going. And you need to grind that inf out.
Do I want sentinels to be better? Yes, Much like I loved the PB changes, I'd like to see something similar for sents, esp since they don't have the flexibility that HEATs have. But until then I'm happy with the sentinel play style. Sentinels aren't blasters. They're not comparable beyond being ranged primary attackers. (See also corrupters and their blast/defemse sets.)
For me, the purpose of sentinels is the play style.
* (Not so) fun fact, to this day I absolutely despise kiting - all because of the fragility of blasters. I don't find it fun at all.
Unrelated side note. I wonder if the disparity is also due to IOs. I mean, original blaster numbers were designed to be decent without set IOs. Set IOs make them way better. Arguably set IOs break the game. Because of that, blasters have their cake and eat yours too. Later power sets and Sentinels were designed with IOs in mind. Almost like set IOs were expected. They seem to play like it.