Play around with this excellent NYT rent v buy calculator to see how your assumptions dictate the huge differences of opinion on whether it's better to rent vs buy:
https://www.nytimes.com/interactive/2014/upshot/buy-rent-calculator.html
I personally am renting and don't consider it as dead money at all.
I look at my friends who bought and if they don't like their job they basically have to suck it up as they need the money for mortgage payments whereas I'm sitting on a relatively large pile of diversified surplus and can walk away whenever I want.
If I decide I want to move to Melbourne (where apartments in the city can be had for under $500k), or offered a job in another country, I can uproot and move easily.
If I decide I want to get a mortgage I can easily liquidate everything and go to the bank.
I'm pretty conservative with debt. Lots of success stories from those who leveraged up and made it work, but I have witnessed the other side of that coin from people who got hurt with debt in the GFC.
If rent is taking up a big chunk of your salary, then rent somewhere cheaper. I rent in one of the suburbs in Sydney which is still pretty cheap (lots of apartments), but has FTTN NBN, new apartment and 30-40 mins to the city where I work by train. Split with my partner.
A term deposit will see me in line with inflation,
A term deposit might match you against what inflation has reported recently, but CPI and other measures are definitionally backwards looking and very lagging. You don't know what future inflation will be without some research and modelling. Additionally, headline inflation may or may not be appropriate for you if you want to buy a house.
Is equities more aligned to those with a house paid off / looking toward the future?
Equities are quite volatile. If you're investing and not trading it's better to think about it like you have $100,000 and you start a small business like a cafe or kebab shop. Every day someone walks past the front door and shouts out a price they might buy the cafe from you. Maybe if they offer $500,000 for the cafe you'd sell it. If they offered you $50,000 you probably wouldn't. Otherwise you just keep going about your business, day in and day out, earning a return from your initial investment and re-investments (like a new coffee machine or bigger shop) you might make over time. You're not interested in the price of the business, but rather what it will return you over a long period of time. Maybe you'll sell it when you retire.