Basic question about Hero Points

So as a newbie at Level 51, warrior, I used my first batch of Hero points to max physical & signet training, and Discipline as a specialization.And have not spent any more accumulated Hero points since acquiring those.Should I continue saving up Hero points to level 80, when I can spend them on Elite specializations?Or is there any reason to spend them now on other specializations (which I may not ever use, because they do not suit my playstyle)?Thanks in advance.

Spend them. I don't think you can spend any on the elite spec until you've maxed the others anyway. Plus, you will have enough from just leveling to 80 to complete everything except for the Elite Specs, without doing any hero challenges. So if you just power leveled from 2 to 80 using Tomes of Knowledge, you'd have enough hero points to complete all the core trait ans skill lines, without doing a single hero point.

Additionally, the Elite specs take a lot of points - 250 each I think, and the HP's in HoT and PoF each provide 10 points, whereas the core HP's only give you 1 point.

If you reach level 80 and you haven't obtained any of the hero points in the open world, you should have enough to unlock every single core utility skill and specialization. Doing map completion of Central Tyria as well as the LWS1 and LWS2 maps like Dry Top and Silverwastes should give you enough hero points to unlock at least 70-80% of one elite specialization.

To sum it all up, you don't need worry about not having enough hero points to spend on a utility skill or specialization trait that you may or may not like. There are plenty of them to unlock both core and elite utility skills and specializations, especially in the Heart of Thorns and Path of Fire zones.

You can't spend any hero points on elite specializations until you've maxed all core specializations. So there's really no reason to hold on to them. Go ahead and spend them on whatever seems interesting to you.

As has been stated, no reason to save until 80.Do focus into specializations so that you can equip full lines though.

In addition to the above, I'd suggest collecting as many HPs as you can while you level. This makes the business of collecting them for an elite spec much quicker. By the time I reach lvl 80 on a toon, I usually have about 180 spare HPs, so that I then only need to complete 7 HP points in HoT or PoF to complete an elite spec. That can be done without any difficulty and in very little time. It's up to you how you level of course, but as far as I'm concerned, as long as you're in need of xp you may as well get it by travelling to and completing HPs, picking up Waypoints, pois, and completing events on the way.