Sadly, the edition war seems to have had a strong influence on the shape of 5e, and I don't think it would be constructive to deny that.
That 5e includes design decisions to favor shorter combats is one of the clearest results of that, and one of the few cases where there was both a clearly-identified problem and a 5e solution (set of solutions, really) that demonstrably worked (in the playtest, at least).
[sblock="combat speed issues"] It's clearly hard to sum up this issue in a quick aside without sounding too much like an edition warrior, so I'll go into it in detail for anyone who cares:
3e, 4e, and 5e have each tried to address complaints about the edition immediately preceding them. In the case of 5e there were complaints that 4e combat was 'too slow.' So, 5e made combats faster in the sense of taking fewer rounds to resolve by lowering monster hps relative to PC damage, making attack rolls succeed more often (and saves fail more often) and reducing options in combat. 4e combat /was/ slower in the sense that the encounter guidelines were centered around larger, more challenging, more involved 'set piece' combats with more tactical options on the player side that took more rounds to resolve. They were also faster in the sense that they were quicker to resolve with fewer rules frustrations and delays than similar combats would have been in prior eds (in which they could be downright problematic, and thus not run that often). A reason for those changes making combat 'slower' was that there had been many complaints that 3e combats were 'static' and lacked meaningful tactical options, and/or devolved into 'rocket tag' in which the side that acted first won in an overwhelming power-combo or SoD or other 'nova' tactic. 3e did end up being 'static' in the sense that the full attack was often the best martial combat option, and precluded movement, and could be deemed 'rocket tag' as there were plenty of ways for a caster to generate untouchable save DCs. Yet, in another sense, 3e /did/ provide many tactical options for both melee types and casters, it's just that, eventually, players found that certain of them (particularly the full attack) were clearly the 'best' options. 3e, of course, had full attacks and complex tactical options (that could be onerous to run through or that proved ineffective or too effective) and boost-able save DCs because complaints had long been made about AD&D that melee types lacked options, that multiple attacks (from Specialization, level & TWFing) were 'broken' and that saves were too easy at high level, making "save: neg" spells virtually useless at those levels.
So, each edition, the game tries to address complaints about the prior edition, only to have new complaints heaped upon it (or even old ones re-hashed). In some cases, WotC so much as openly identifying the complaint that a mechanical change addressed led to push-back and complaints from outraged fans. [/sblock]
Given that there was strong demand for faster combat with some basis in fact, in part fueling the edition war (which, hopefully, we don't want to repeat), and that 5e made changes that delivered faster combats, those changes /need/ to be understood in that context and *cut some serious slack.*
That could very well include putting up with a few character deaths at 1st level (or just starting at 3rd, which is a very effective, and IMHO, perfectly reasonable solution that the OP dismissed out of hand). And it's obvious how shorter combats (in rounds) could increase the importance/impact of surprise rounds. So even if the OP doesn't want high-impact surprise rounds, he should consider the context that has led to them.