He'll spend well over $2k building a custom rig.
Most prices for the items on your list are too low, unless you are working on crc pricing.
Ie. Headset and bb, more like $40 each.
Decent pedals, $80+
Tyres and tubes, more like $150.
Bars and stem - $100++ (Most short length stems are well over $50, if not $100 or more.)
New frame off the shelf, more like $600+
So sure, you can make a custom for under $2k... that still needs upgrades.
but do you really
need them?
you need to know where to spend money and where you can go a bit cheaper. stems, front hubs, seats, posts etc you can cheap out on, even tyres and grips and brakes, if you even need them at all.
also speccing bmx style components is usually cheaper. 22.2mm stems, bmx hubs, bmx cranks, are usually cheaper than mtb equivalents, for the same quality. theres a much bigger market fox bmx than for dj/street hardtails so the parts are more common, and the prices are lower. tyres and tubes? try $100 instead of 150. maxxis dth and standard run of the mill tubes. pedals? $50 and get some odyssey trailmixes, or even spend half that for a fly ruben graphite, which is a fibreglass blend pedal, hich is extremely strong for a composite material and i bent the axle on mine before the pins even wore out, 18 months after i bought them for $20. this is all at rrp by the way, so you can go down to your local shop and order this stuff at the same price, if its a bmx shop they should have some trialmixes or rubens in stock, very popular pedals.
you can get brand new Pride Street frames, in either bmx or mtb spacing, for about $300 posted direct from the manufacturer, and they are post weld heat treated 4130 with multiple butted tubes. they do cheap bars too, and if you are manly enough to run a rigid, they make a fork, as well as sprockets, pedals, etc. if you arent going to support local businesses, at least support people who care about dj and street and arent just in it to make some money. NS also make good parts like the district/proof bars and their rims are pretty good too.
going back to the local shop thing,
before i worked in a shop i got 90% of my bmx stuff through one shop. i got to see the parts close up before i bought them, got answers about compatibility straight away, and once you factor in shipping, it was cheaper to just buy it from the shop. and i walk out with the part in my hands so i could go ride that afternoon. not too long ago i saw someone bought a frame online, and half the frame wasnt even welded. as in there was nothing holding the tubes together on the drive side of the frame. in that situation you have to spend $100+ sending it back to the dealer (which in most cases, is non refundable. postage to the UK is almost as much as i paid for my frame alone), screwing around with emails and warranties etc. at a local shop, thats taken care of for you. usually even before we sell you the frame, part etc.