Really everyone is desperate to marry the farmer or get out of the valley in general but will settle for the farmer as they are the newest addition in to Stardew valley since they got sucked into its land of no return. Penny does have added emotional needs, but they are all depressed once they get stuck as a housewife/househusband day after day. They end up staring at statues or lights all day every day they aren’t visiting family or on ginger island. But that’s better than what they had before…right?
Sorry, but no.
Maru is, so far as I can tell, Ace. She expresses no romantic interests in the Farmer, and has no need or desire to leave her current residence or the valley as her father is supportive of her scientific endeavors. Even at ten hearts, the best the Farmer can manage is 'lab assistant' or 'project partner'. She has a valuable job as a Nurse at the local clinic, she has personal fulfillment in her projects, she has the loving support of her family. She is not 'desperate' for anything.
Emily isn't 'desperate' for anything. She's living her life, quite content with what she has. Sure, she marches to the beat of a different drum, but in a world in which magic and spirits definitively exist, who's to say she's not closer to the truth than the majority of citizens? She's got so much zen going on that she's genuinely comfortable with her life. She accepts the Farmer's interests if they are expressed, and decides to include the farmer in her life for herself. However, as we can see from her non-reaction to Clint, she's also certainly not eager to jump at the first chance she gets. It's a surprisingly healthy mental attitude, really.
Hailey is desperate for
attention, not escape. Her parents effectively abandoned her, the only person who hasn't is her sister. So she builds herself up as something of value so that she won't be discarded again. Which isn't a very healthy mental image, viewing yourself as an object of value instead of a person, but one that is all too common. Hailey is one of the few romantic candidates who actually has character development through the relationship plot. She realizes that she is a person and has self-worth, and realizes she doesn't have to keep up the princess facade. Which is a much healthier mindset to approach a relationship from.
Leah is not 'desperate' for anything either. She likes her current life. She is free of her controlling and manipulative ex, free to roam the valley, free to create art and express herself. One of the things I like about her plotline is that you the farmer *help* her without *taking over* for her. You support her in her endeavors, but they are *her* endeavors, not yours. She respects that, and a genuine friendship blooms before romance does. You can step back and let *her* deal with her ex, you don't have to come to her rescue, she's quite capable of doing so herself, thank you very much. And it is from that position of internal strength that she decides that the Farmer is someone she wants to get to know better.
Abigail is desperate to get away from her father. Not because of abuse, although he is rather neglectful, but out of a childish rebellion befitting a young teen, not a twentysomething. She acts like a kid, and he treats her like one. This is not a healthy dynamic for either of them. However, much as she claims to yearn for adventure, what she actually wants is her idealized dream of adventure, which mostly boils down to 'being away from her father'. As seen in her ten heart event, actual adventure terrifies her. Her mother at least cares for her, and helps her as best she can. Her father is too busy running his business to recognize what is going on, a common failing in sole proprietorships. Honestly, she's almost as much a brat as Hailey, but without the character development arc. She starts acting like a rebellious teen, and ends her ten heart event acting like a rebellious teen.
I don’t like the scene with George, but we all make mistakes. Her intentions were good, she just messed up. She’s very generous being the only adult in the whole valley willing to tutor the only children in the place so remote it doesn’t even have a formal public school. She also takes them to the playground and occasionally ginger island in between school days so they don’t have to wait for auntie Marnie to stop staring at the microwave or auntie or uncle to get home from the bar, or hear their mom freak out about more messes to clean or dirty hands from digging in the dirt looking for bugs. She also goes through abuse emotional (and likely physical) beyond belief and has likely PTSD nightmares and flashbacks of her father that are even worse. So even though she appears weak, she is incredibly strong. She doesn’t even have a counselor to work through her issues with, she’s doing it all on her own. I’m a fan of hers. I’m straight so I wouldn’t marry her but I would have her as a roommate like Krobus while she waits for Sam to work up the courage’s to ask her to marry him.

She needs a counselor to work through her issues with, not a life partner to dump on.
Honestly, her and Sam would end horribly. Sam doesn't have the maturity to understand what is going on in Penny's head and is likely to take things at face value. He doesn't have a career path to support a family, which Penny desires. He's stuck in a dead end job with no hope of advancement, and without even the realization that he's already pidgenholed himself into that role. He's a nice guy, but he wouldn't understand what Penny needs vs what she says she needs. Sam is basically a younger Shane that hasn't sunk into the bottle yet. And the combination of trying to work double shifts to keep food on the table and a roof over their head plus Penny's emotional needs that she *won't* openly discuss, is going to drive him there.