I haven't spent nearly as much time looking at rifles as I have spent researching calibers. Nobody worth his own salt would disagree with the fact that the .30-06 is an incredibly versatile round. That doesn't mean it's the best round for any given context, because it's not, but a 6.5 cannot "do everything better." There are only trade-offs, there is no perfect round. I am not fully committed to the .30-06 - I'm open to suggestions, but it's a solid choice when the trade-offs of every round are taken into consideration.
Its versatility is appealing to me. It has manageable recoil compared to the magnum rounds, yet it is an appropriate hunting round for everything in North America short of coastal browns or inland grizzlies. What caliber would recommend instead?
The 30-06 is fine, but it’s not particularly versatile or light recoiling in a lightweight rifle. My T3X lite with an SWFA 3-9 shooting 175-180 gr bullets gets uncomfortable rather quickly, and there’s no way in hell I’m spotting impacts. The only thing it does better than a 6.5 prc, 280ai/7 saum, 6.8 western, etc., is shoot very heavy bullets anemically slow, which I’ll touch on below.
With the right bullet selection, those above will kill elk (or anything else) just as dead, at longer ranges, and with less recoil (other than the 6.8 western, which will recoil as much or more). A significant recoil reduction will make you more likely to practice adequately, and the higher MV and BC will give you a much larger margin of error in range and wind estimation. If you were a reloader and wanted to hot rod something in the 200-215 gr area in the 06, the difference wouldn’t be as significant. That would come at the cost of recoil, and you still end up with marginal velocity. You mentioned you don’t load, so none of that is relevant. It also doesn’t matter what twist rate a tikka has, as you probably won’t find factory .308 or 30-06 ammo over 180 grains.
If someone really wanted to look at the significance of these differences, the WEZ calculator would be great for looking at the difference in hit rates. I’m lazy, so I’ll just give a quick comparison of Federal’s claimed wind drift (10mph full value) at 400 yards with 6.5 PRC, 280 AI, and 30-06 Terminal Ascent factory ammo. 9.6 inches, 8.9 inches, and 11.4 inches, respectively. If that seems small, just remember you’re stacking tolerances. Getting an advantage where you can matters.
As I alluded to earlier, if the desire is heavy, high BC .30 cal bullets, there are plenty of great magnum cartridges to choose from.
All that said, I didn’t recommend other cartridges because I dislike the 30-06. It just opens up options such as Fierce and Seekins. Both make nice rifles with reasonable weights and ergonomical stocks. The latter is still hard to find in a factory hunting rifle.
Thinking about it more, I would probably avoid going high dollar on a first big game rifle. After a year or two using it you’ll know much more about what you like or dislike. The nice thing about a cheap tikka is that you can add a vertical grip and cheek riser for $75 and 30 minutes of your time. No need to feel bad drilling holes into their cheap Tupperware stock, and painting it can be a fun project. Back to the recoil, allotting ~$1k of your budget to a nice can would also be a great option. If you do end up with a lightweight 30-06, I’d really recommend either a suppressor or brake. Range sessions would be more comfortable, and follow up shots would be faster.
Good luck in your search, I hope you find what fits your needs. There’s plenty to choose from. FWIW, the Bushnell LRHS/LRTS scopes are very impressive for the price and worth consideration.