Here are a few points that might help you get a better sense of all the bells and whistles in your question:
1) Structure of Sell Side Desks
From a Sell Side perspective (Market Maker) its common to have Risk Specialization/Segmentation across desks, this is important because it determines which factor you're responsible to trade and profit from... all other factors are usually hedged internally with the respective desks in charge of each exposure, this is done to streamline risk management, capital allocation and to maximize deal flow within the company.
To give you an idea of what the above looks like... with a simple equity option you'll have an options desk that'll trade the Volatility, a Spot desk that will handle the Delta Risk and a Futures/STIR desk that will be concerned with Dividend and Interest Rate risk. This is a simplified version of how the structures look like but you get the idea/principle.
Why is this relevant? well because the Derivatives trader himself might not go to the market to hedge the Repo Rate exposure, but rather toss it over to his colleague in the STIR/Futures/Money Market Desk for him to handle and profit from.
2) Repo Spreads instead of Rates
Rather than thinking about a Repo rate, think of if as a Repo Spread... the rates are anchored on a Risk-Free* rate curve, and on top of it you overlay the extra risk associated with entering into Security Finance transactions with a given security/Basket/Index, just like the risk-free rate there's a term structure (curve) and a bid-offer for this spread (same with dividends).
To illustrate this simply take the price of the spot and futures at different maturities and compute the implied repo rate for equities with different levels of liquidity/Short Volume, compare that to the OIS quotes.
Again, why is this relevant? well, you can pretty safely say you will be able to hedge your position or be indifferent* to the risk free rate... this is not so true for the Repo Spread so you have to keep an eye on it.
3) Who's paying for all of this? Shareholder Finance
There're strict risk management and capital controls within the Sell-Side, this basically means there's regulations that state that for each unit of risk the bank must set aside a slice of un-invested capital/cash as a buffer for losses, this is to safeguard the stability of the market etc... now, since the shareholders of the institution parked money as a capital buffer they're going to ask you to make sure you make it worth their while by charging you a cost of capital rate... because hey, they could be spending that money financing projects or other profit centers rather than setting it aside as a cushion for your trading, this is what falls under the umbrella of transfer pricing, XVA (FVA in particular) and general ALM.
Why is this important? well, you asked: "Hum yeah, but what if you don't borrow from another department, or that you don't borrow at all ? isn't this possible ?" indeed, its possible you don't borrow from another department at all and you just go into a naked derivatives position, and hell, you might even make a lot of money... but the PnL you see on the screen is not going to be the bar with which you'll be measured, this will have a bunch of deductions one of which is the pure cost of capital as Noob and Kurtosis pointed out.
4) The Buy Side
There is big business behind this Repo Spread, Buy side institutions such as pension funds, are some of the biggest holders of long term equity inventory, they use securities lending as a way to improve the retuns, hedge and finance operations.
Market prices (as you can check from the suggestion in 2)) are already considering this risk factor, if as a market maker you price without it regardless of whether you're hedging it or not, you'll be leaving money on the table and opening yourself to being arbitraged or just generating noncompetitive prices, this might or might not be too significant depending on the market profile in terms of liquidity bid-offer.