Yes DM's can bridge the gap, by throwing stats at the monk earlier, but by raw the cost of most monk ac buffing items are over 2000 gold in a system that doesnt hand out more than 100 gold for most quests under lvl 7.
5th edition doesn't really work that way though, the class is supposed to carry most of its own power your really only supposed to get about 3 magic items of any real power ..... any non monk can throw on platemail and not lose thier class abilities simply by being proficient, monk literally loses thier whole class for throwing padded armor on .... or a shield. Those two items dont need to be magical to outscale the monks entire build history from level 1 to 20. A level one fighter with platemail and a shield will have higher ac than a monk of tremendous level, beyond even the scope of this game. Thats a 22 at lvl one for another front liner that can stay pretty close on damage, or be equal if they drop to 20 only 4 points off your lvl 20 max for monk.
The underbalance of monk is almost as egregious as the underbalance of ranger.
what you are siting when you say "just multiclass into warlock" is actually "just multiclass into one of the best damage dealers in the game and basically be a warlock and more valuable as a warlock than several levels of monk provide. if you are a lvl 3 monk and lvl 1 warlock almost 50% of your damage comes from warlock ..... that shouldn't be the case.
