Feat tax to get a subclass to work, and that cast + attack comes at the cost of all your extra attacks... still fails to impress me..
No feat tax. Withdrawing or stowing a weapon is a 'free' action. But with the feat it's not needed, but you gain the ability to cast as opportunity attack and advantage to concentration. Casting isn't necessary to make an eldritch actually super good at combat, but it offers him the versatility and flavor of caster without the penalty many of the gish classes take to DPR.
It's his available slots that are the problem, as he will get 3rd level spells when there's already Forcecages and such starting to fly around. It just seems like anyone could accomplish the same by carrying a few scrolls around.
Not seeing the pervasiveness of scrolls in this as may have been in other editions.
Not to mention that it'd still be better to just keep blasting with Eldritch Blast in most melee, if Eldritch Blast is what you've spent your resources on. Because you don't need to spend invocations on getting multiple attacks with it, and if it's just one melee enemy, you can push them back with the first hit (as you have the knockback Invocation, if this is your focus). 4 attacks at disadvantage and all your boost focus (Invocations, Hex) on them is better than 2 attacks without disadvantage.
Warlocks get 8 invocations. Not sure the 'expense' of 1 or 2 invocations is necessarily a drag for someone who wants it. The solution you present, spend another invocation on Eldritch, so that you don't have to spend one on blade doesn't make the advantage any clearer. What if there are two enemies? or three within 5'? What about cover? More over, the real numerical advantage of Eldritch blast in close combat (within 5') becomes significant at level 17, and only then. Why not just swap out your blade pact invocations for other ones then?
More to the point, the OP is asking for good gish options, not 'show me a gish option where mixed melee and casting is the absolute most optimal way to play'. A blade pact warlock that takes a couple point DPR reduction at mid-levels so that he can do both isn't 'wasting his time.
And if the Eldritch Blast has to deal with cover (which the opponent will get pushed out from with the first successful hit), that means he is at a range where the sword could not reach the enemy at all, so... I'm not sure how that factors in.
Well, if they have cover, say shooting through an open window.... You run up, and stab him through the open window.
Honestly, Bards get enough spell copying to pick up smites and whatever else spells they want. Valor is the fighter/mage option, but Lore is the stronger option (because it gets to copy more stuff and earlier). I just think they can solve most cases by going through their spells first, then using physical attacking as the last 'nah, cannot be bothered to spend any of my hundred slots on this' resort, because they ARE full casters. And if they have slots available, and the melee situation IS an actual threat, well, melee proximity doesn't hinder spells with save.
Again, lore may be a better option (and I'm not sure that it is), but in the same way a free Dinner with desert may be better then a free dinner, but in this case the OP isn't looking for desert. He looking for gish style class, and Valor is better at that.
Ranger doesn't get much, and besides most of what he gets, isn't exactly magical. Like, shoot many arrows as their lv5 spell, such magics.
I disagree. Ranger get some amazing spells, (some seemingly balanced for ranger's level not druids). Lightning arrow, Spike Growth, and Conjure animals to name a few.
Monk does have the elemental path, which might work for OP's criteria. Admittedly, it looks weak (just different variants of elemental blasts), but yeah, it should count. Curious to see if people can make that work.
Monks, like many of the classes have subtle combinations built into the full range of their abilities that combine really effectively. An ongoing Gust of Wind, combined with a guy that that can essentially move 80' a round and still take an action is pretty good. Add in the mobility feat and a monk can continuously attack and runaway, with few things being able to get to him.